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Dissertations / Theses on the topic 'Negativity quantum field theory'
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1
Oeckl, Robert. "Quantum geometry and Quantum Field Theory." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621912.
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Gupta, Neha. "Homotopy quantum field theory and quantum groups." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/38110/.
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The thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one (Chapter 3) of the thesis generalises the definition of an n-dimensional HQFT in terms of a monoidal functor from a rigid symmetric monoidal category X-Cobn to any monoidal category A. In particular, 2-dimensional HQFTs with target K(G,1) taking values in A are generated from any Turaev G-crossed system in A and vice versa. This is the generalisation of the theory given by Turaev into a purely categorical set-up. Part two (Chapter 4) of the thesis generalises the concept of a group-coalgebra, Hopf group-coalgebra, crossed Hopf group-coalgebra and quasitriangular Hopf group-coalgebra in the case of a group scheme. Quantum double of a crossed Hopf group-scheme coalgebra is constructed in the affine case and conjectured for the more general non-affine case. We can construct 3-dimensional HQFTs from modular crossed G-categories. The category of representations of a quantum double of a crossed Hopf group-coalgebra is a ribbon (quasitriangular) crossed group-category, and hence can generate 3-dimensional HQFTs under certain conditions if the category becomes modular. However, the problem of systematic finding of modular crossed G-categories is largely open.
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Poletti, Stephen John. "Geometry, quantum field theory and quantum cosmology." Thesis, University of Newcastle Upon Tyne, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315921.
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Kerr, Steven. "Topological quantum field theory and quantum gravity." Thesis, University of Nottingham, 2014. http://eprints.nottingham.ac.uk/14094/.
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This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a 1-manifold. The models are independent of the triangulation and give the same result as the continuum partition functions evaluated using zeta-function regularisation. Some implications for more physical models are discussed. In the second part, the gauge gravity action is written using a particularly simple matrix technique. The coupling to scalar, fermion and Yang-Mills fields is reviewed, with some small additions. A sum over histories quantisation of the gauge gravity theory in 2+1 dimensions is then carried out for a particular class of triangulations of the three-sphere. The preliminary stage of the Hamiltonian analysis for the (3+1)-dimensional gauge gravity theory is undertaken.
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Ivin, Marko. "Topics in quantum field theory." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410042.
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Russell, I. H. "Calculations in quantum field theory." Thesis, University of Newcastle Upon Tyne, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328134.
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Rondelli, Andrea. "Functional methods in quantum field theory." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15839/.
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Iniziamo introducendo l'integrazione su manifold di Hilbert, tramite l'approssimazione dello spazio tangente alla varietà. Passiamo poi a descrivere due tecniche per regolarizzare integrali funzionali o di cammino quadratici (che presentano un laplaciano nell'azione): la regolarizzazione e rinormalizzazione tramite zeta function e il cutoff nel tempo proprio. Cerchiamo di confrontare i due diversi risultati (finiti) così ottenuti. Sussessivamente applichiamo l'integrazione funzionale agli integrali di cammino usando il formalismo della quantizzazione in qp-simboli ottenendo così un'ampiezza di probabilità. Infine iniziamo a sviluppare questi argomenti per le teorie di gauge. In particolare ci soffermeremo su vari aspetti geometrici dei campi di gauge, quali la connessione e la curvatura (usando il formalismo dei fibrati). In ultimo introduciamo l'integrazione funzionale per le teorie di gauge.
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at, Andreas Cap@esi ac. "Quantum Field Theory as Dynamical System." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1055.ps.
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Mazur, Daniel Paul. "Nonperturbative quantum field theory in astrophysics." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/43255.
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The extreme electromagnetic or gravitational fields associated with some astrophysical objects can give rise to macroscopic effects arising from the physics of the quantum vacuum. Therefore, these objects are incredible laboratories for exploring the physics of quantum field theories. In this dissertation, we explore this idea in three astrophysical scenarios.
In the early universe, quantum fluctuations of a scalar field result in the generation of particles, and of the density fluctuations which seed the large- scale structure of the universe. These fluctuations are generated through quantum processes, but are ultimately treated classically. We explore how a quantum-to-classical transition may occur due to non-linear self-interactions of the scalar field. This mechanism is found to be too inefficient to explain classicality, meaning fields which do not become classical because of other mechanisms may maintain some evidence of their quantum origins.
Magnetars are characterized by intense magnetic fields. In these fields, the quantum vacuum becomes a non-linear optical medium because of interactions between light and quantum fluctuations of electron-positron pairs. In addition, there is a plasma surrounding the magnetar which is a dissipative medium. We construct a numerical simulation of electromagnetic waves in this environment which is non-perturbative in the wave amplitudes and background field. This simulation reveals a new class of waves with highly non-linear structure that are stable against shock formation.
The dense nuclear material in a neutron star is expected to be in a type-II superconducting state. In that case, the star’s intense magnetic fields will penetrate the core and crust through a dense lattice of flux tubes. However,
depending on the details of the free energy associated with these flux tubes, the nuclear material may be in a type-I state which completely expels the field. We compute the quantum corrections to the classical energies of these flux tubes by creating a new, massively parallel Monte-Carlo simulation. The quantum contribution tends to make a small contribution which adds to the classical free energy. We also find a non-local interaction energy with a sign that depends on the field profile and spacing between flux tubes.
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O'Donald, Lewis John. "Twistor diagrams and quantum field theory." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306032.
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Daniels, D. R. "Quantum field theory near black holes." Thesis, Swansea University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636346.
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In Part I we investigated the phenomenon that photons propagating in curved space-time may, depending on their direction and polarisation, travel at speeds greater than the speed of light <I>c</I>. The explicit cases calculated for, were the Reissner Nordstrom and Kerr metrics. This led to a postulated Horizon Sum Rule and Polarisation Theorem for photons propagating in general black hole spacetimes. The effects of a purely electromagnetic background were also calculated on photon propagation, with an intriguing possible link with the conformal anomaly appearing. We argue that the 'faster than light effect' does not violate causality, but rather implies the breakdown of the Strong Equivalence Principle for interacting Quantum Field Theories in curved space-time. In Part II we calculated the tree level and one loop quantum corrections, to the entropies of Rindler space and a Schwarzschild black hole, in two dimensions, due to a minimally coupled, massive scalar field, via two differing approaches. The first, the conical singularity method, relied on shifting the Hawking temperature away from its equilibrium value, inducing temperature dependent corrections to the entropy. For the Schwarzschild black hole case, the effective action was found to possess the property of invariance under temperature duality. The second, 'Brick Wall' method, involved counting the number of states that a scalar field could occupy in the vicinity of an event horizon. The entropies consequently obtained for Rindler space and a Schwarzchild black hole, in two dimensions, were found to be divergent as the horizon was approached. We discussed how both investigations might shed some light on the nature and origin of black hole entropy.
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Cassidy, M. J. "Quantum field theory and acausal spacetimes." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597360.
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This thesis is concerned with various problems that arise when one attempts to quantise fields on spacetimes which contain regions of closed time-like curves (CTCs). Chapter 1 presents a review of some of the major classical and quantum difficulties encountered by various authors investigating acausal spacetimes until 1993. In chapter 2, a number of more recent proposals that have been put forward in an attempt to construct a consistent dynamics are considered. Particular consideration is given to the density matrix proposal for Deutsch and Politzer, which is ultimately shown to give a nonlinear evolution through the acausal region. This work has been published in Phys. Rev. D 52, 5676 (1995). The chapter concludes with a discussion of the Euclidean approach, which is adopted by this author for much of the remainder of the thesis. It is argued that the inevitable loss of quantum coherence is physically preferable to the nonlinear evolution encountered in the other proposals. Chapter 3 is concerned with the effective action for matter fields defined on acausal spacetimes, in which an expression is derived for the 1 loop effective action for fields for arbitrary mass and spin on Euclidean spaces which have acausal analytic continuations. I will show that in general, after one has analytically continued back to the acausal section, the effective action diverges to minus affinity at each of the <I>n</I>th polarised hypersurfaces of the spacetime with a structure governed by a de Witt-Schwinger type expansion. In particular, I will show that even if →<I>T<SUB>μν</SUB></I>π remains finite at the Cauchy horizon, the effective action will still diverge there. This work has been published in Classical and Quantum Gravity 14, 3031 (1997). In chapter 4 I attempt to give a sensible interpretation to Euclidean path integrals in the presence of causality violations, which was work carried out in collaboration with S.W. Hawking. If the action always diverges to minus infinity, then at first sight it seems as if any Euclidean path integrals will be completely ill defined. However, I will argue that if one focuses on the density of states, one can obtain physically reasonable results. Ultimately, I will derive an expression for the effective action of a boosted scalar field configuration in the product of three dimensional de Sitter space and <I>S</I><SUP>1</SUP>, and I consider the number of states with a fixed linear momentum around the <I>S</I><SUP>1</SUP> as the particles are given more and more boost momentum. I will show that at the critical point when the spacetime is about to develop closed timelike curves, the number of states tends to zero. This suggest that quantum mechanics naturally enforces the Chronology Protection Conjecture by superselecting the causality violating field configurations from the quantum mechanical phase space. This work has been accepted for publication in Phys. Rev. D. Finally, in chapter 5 I consider what happens when one includes the effects of back reaction in a spacetime containing CTCs. Misner space is considered as an axisymmetric Bianchi I universe and it is assumed that near the horizon, the periodic identification in the <I>x</I> direction provides the dominant contribution to the energy-momentum tensor. I will show that, as the horizon is approached, any small perturbation grows until a singularity forms in a finite proper time, which therefore lends further support to the Chronology Protection Conjecture. This work has been submitted for publication to Classical and Quantum Gravity and is the subject of DAMTP preprint R/98/01.
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Dolan, F. A. "Aspects of superconformal quantum field theory." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.598582.
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Various Issues in Superconformal Quantum Field Theory in (mainly) four dimensions for <i>N </i>= 1,2,4 are discussed. Broadly these issues concern the constraints placed on scalar four point functions by superconformal symmetry and the information that they give concerning the operator product expansion. Where possible this information is verified from the point of view of three point functions (for <i>N = </i>4) and of superconformal representation theory for <i>N </i>= 2,4. For <i>N </i>= 1 the chiral superfield four point function is computed and verified in a number of ways; involving a counting argument and superconformal integrals and from the point of view of the operator product expansion. For <i>N = </i>2 two point functions for fields in the simplest non-trivial supermultiplet and four-point functions involving the scalar quasi-primary fields of this supermultiplet are discussed. For <i>N </i>= 4 the simplest supermultiplet containing the energy momentum tensor is similarly considered as for <i>N </i>= 2. Two point functions and three point functions, up to the energy momentum tensor three point function, are computed. Four point functions of the scalar quasi-primary fields (corresponding to chiral primary operators of scaling dimension 2) for this <i>N </i>= 4 supermultiplet are also investigated, revealing an interesting struture implied by superconformal symmetry and the operator product expansion. The operator product expansion is applied to these various scalar four point functions in the disguised form of a conformal partial wave expansion. A new method is applied and a new result in four dimensions is found for the conformal partial wave expansion. This result proves particularly useful for extracting detailed information about the operator product expansion contained in four point functions in four dimensions. It is also useful for extracting anomalous dimensions of operators as is done for the <i>N </i>= 4 chiral primary four point function at weak and strong coupling. The strong coupling result derives from the AdS/CFT correspondence and reveals interesting information which demonstates the decoupling phenomena for large 't Hooft coupling and large <i>N </i>from a purely algebraic viewpoint.
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Ellicott, Paul. "Geometrical aspects of quantum field theory." Thesis, University of Newcastle Upon Tyne, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329154.
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Flachi, Antonino. "Quantum field theory on brane backgrounds." Thesis, University of Newcastle Upon Tyne, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366586.
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Smith, C. J. "Energy conditions in quantum field theory." Thesis, University of York, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434155.
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Razzaghe, Ashrafi Babak 1964. "Making and remaking quantum field theory." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29762.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Program in Science, Technology and Society, 2003.<br>Includes bibliographical references (leaves 139-156).<br>In this thesis, I examine two episodes in the history of quantum field theory using different research techniques and historiographic approaches. The first episode occurred during the 1920's and 1930's when quantum mechanics and relativity were being reconciled. I present some of the central developments of that episode using an approach that relates questions asked by physicists to the structures of putative natural kinds upon which they predicated their research. The second episode occurred during the 1960's and 1970's when important features of quantum field theory were given new interpretations that arose from the exchange of methods and insights between particle physics, solid state physics, statistical mechanics and physical chemistry. Research for the second episode was conducted in collaboration with other historians and scientists using novel web-based and database-backed research tools.<br>by Babak Razzaghe Ashrafi.<br>Ph.D.
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Lifschytz, Gilad. "Quantum gravity and topological field theory." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/33529.
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Olbermann, Heiner. "Quantum field theory via vertex algebras." Thesis, Cardiff University, 2010. http://orca.cf.ac.uk/54994/.
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We investigate an alternative formulation of quantum field theory that elevates the Wilson- Zimmermann operator product expansion (OPE) to an axiom of the theory. We observe that the information contained in the OPE coefficients may be straightforwardly repackaged into "vertex operators". This way of formulating quantum field theory has quite obvious similarities to the theory of vertex algebras. As examples of this framework, we discuss the free massless boson in D dimensions and the massless Thirring model. We set up perturbation theory for vertex algebras. We discuss a general theory of perturbations of vertex algebras, which is similar to the Hochschild cohomology describing the deformation theory of ordinary algebras. We pass on to a more explicit discussion by looking at perturbations of the free massless boson in D dimensions. The perturbations we consider correspond to some interaction Lagrangian P(<p) = A Cp if. We construct the perturbations by exploiting the associativity of the vertex operators and the field equation in perturbative form. We develop a set of graphical rules that display the vertex operators as certain multiple series reminiscent of the hypergeometric series.
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O'Connell, Donal Wise Mark B. Wise Mark B. "Unusual signs in quantum field theory /." Diss., Pasadena, Calif. : California Institute of Technology, 2007. http://resolver.caltech.edu/CaltechETD:etd-05242007-141715.
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Sprickerhof, Jakob. "Causal structures in quantum field theory." Thesis, University of Leeds, 2015. http://etheses.whiterose.ac.uk/10658/.
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In this dissertation, I will argue that quantum field theory can be interpreted as a description of causal interactions. I will first discuss previous theories of physical causation, and come to the conclusion that they are inapplicable in quantum field theory. As a consequence, I will start to develop a new theory of causation by first analysing the concept ‘causation’ into the most basic and widely shared intuitions, in order to find out later whether these intuitions can be reduced to physics. I will then have a closer look on the intuition that causation is a directed relation, which is commonly regarded as incompatible with the symmetries of physics. I will present a new argument to the effect that causation and quantum field theory are compatible with respect to the directionality of causation. After that, I will analyse the theoretical description of interactions in quantum field theory, and in particular group structure, locality and local conservation laws will crystallise as the central concepts that a causal interpretation might be based on. Subsequently, I will discuss and present replies to what I believe are the most relevant objections to a causal interpretation of physics, namely, Haag’s theorem, the measurement problem and entanglement. In the final chapter of this dissertation, I will conjoin the results of the previous chapters to a new theory of causation for quantum field theory. The main result will be that a causal process is a quantum field theoretical interaction, i.e., the exchange of energy from an initial to a final state via a force.
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Di, Mauro Marco. "Flavor mixing in quantum field theory and quantum information." Doctoral thesis, Universita degli studi di Salerno, 2011. http://hdl.handle.net/10556/194.
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2009 - 2010<br>After reviewing the formalism for describing flavor mixing, both in Quantum Mechanics
and Quantum Field Theory, some consequences along three different directions are studied.
First, it is proposed that flavor mixing can be a viable candidate for spontaneous
supersymmetry breaking, due to the nontrivial vacuum structure induced by it. After
the statement of the conjecture, an explicit proof in a simple case is given. Second, the
properties of flavor states as entangled states both in QM and QFT are studied. By interpreting
such states as multipartite mode–entangled states, both the correlation content and
the decoherence effects are studied. Third, a possible new interpretation of flavor mixing
as induced by an external vector field is proposed, and it is shown how this solves some
problems of the usual formalism in connection with Lorentz and Poincar´e violation. Some
phenomenological consequences of this picture are pointed out, as well as some intriguing
physical interpretations. [edited by author]<br>IX n.s.
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Eakins, Jonathan Simon. "Classical and quantum causality in quantum field theory, or, "the quantum universe"." Thesis, University of Nottingham, 2004. http://eprints.nottingham.ac.uk/10069/.
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Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is represented by a pure state wavefunction contained in a factorisable Hilbert space of enormous dimension, and where this statevector is developed by successive applications of operators that correspond to unitary rotations and Hermitian tests. Moreover, because by definition the Universe contains everything, it is argued that these operators must be chosen self-referentially; the overall dynamics of the system is envisaged to be analogous to a gigantic, self-governing, quantum computation. The issue of how the Universe could choose these operators without requiring or referring to a fictitious external observer is addressed, and this in turn rephrases and removes the traditional Measurement Problem inherent in the Copenhagen interpretation of quantum mechanics. The processes by which conventional physics might be recovered from this fundamental, mathematical and global description of reality are particularly investigated. Specifically, it is demonstrated that by considering the changing properties, separabilities and factorisations of both the state and the operators as the Universe proceeds though a sequence of discrete computations, familiar notions such as classical distinguishability, particle physics, space, time, special relativity and endo-physical experiments can all begin to emerge from the proposed picture. A pregeometric vision of cosmology is therefore discussed, with all of physics ultimately arising from the relationships occurring between the elements of the underlying mathematical structure. The possible origins of observable physics, including physical objects positioned at definite locations in an arena of apparently continuous space and time, are consequently investigated for a Universe that incorporates quantum theory as a fundamental feature. Overall, a framework for quantum cosmology is introduced and explored which attempts to account for the existence of time, space, matter and, eventually, everything else in the Universe, from a physically consistent perspective.
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Farhi, David. "Jets and Metastability in Quantum Mechanics and Quantum Field Theory." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:26718743.
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I give a high level overview of the state of particle physics in the introduction, accessible without any background in the field. I discuss improvements of theoretical and statistical methods used for collider physics. These include telescoping jets, a statistical method which was claimed to allow jet searches to increase their sensitivity by considering several interpretations of each event. We find that indeed multiple interpretations extend the power of searches, for both simple counting experiments and powerful multivariate fitting experiments, at least for h->bb at the LHC. Then I propose a method for automation of background calculations using SCET by appropriating the technology of Monte Carlo generators such as MadGraph.
In the third chapter I change gears and discuss the future of the universe. It has long been known that our pocket of the standard model is unstable; there is a lower-energy configuration in a remote part of the configuration space, to which our universe will, eventually, decay. While the timescales involved are on the order of 10^400 years (depending on how exactly one counts) and thus of no immediate worry, I discuss the shortcomings of the standard methods and propose a more physically motivated derivation for the decay rate. I then make various observations about the structure of decays in quantum field theory.<br>Physics
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Hättich, Frank. "Whitehead's process philosophy and quantum field theory." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969348061.
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Borris, Markus. "Quantum Field Theory on Non-commutative Spacetimes." Doctoral thesis, Universitätsbibliothek Leipzig, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-67788.
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The time coordinate is a common obstacle in the theory of non-commutative (nc.) spacetimes. Despite that, this work shows how the interplay between quantum fields and an underlying nc. spacetime can still be analyzed, even for the case of nc. time. This is done for the example of a general Moyal-type external potential scattering of the Dirac field in Moyal-Minkowski spacetime. The spacetime is a rare example of a Lorentzian non-compact nc. geometry. Elements of the associated spectral function algebra are shown to be operationally involved at the level of quantum field operators by Bogoliubovs formula.
Furthermore, a similar task is attacked in the case of locally nc. spacetimes. An explicit star-product is constructed by a method of Kontsevich. It implements a decay of non-commutativity with increasing distance. This behavior should benefit the technical side - diverse interesting formal attempts are discussed.
It is striven for unification of several toy models of nc. spacetimes and a general strategy to define quantum field operators. Within the latter one has to implement the usual quantum behavior as well as a new kind of spacetime behavior. It is shown how this two-fold character causes key difficulties in understanding.
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Schmidt, Robert. "Defects in Higher-Dimensional Quantum Field Theory." Diss., lmu, 2007. http://nbn-resolving.de/urn:nbn:de:bvb:19-71937.
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Comeau, Marc A. "Premonoidal *-Categories and Algebraic Quantum Field Theory." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/22652.
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Algebraic Quantum Field Theory (AQFT) is a mathematically rigorous framework
that was developed to model the interaction of quantum mechanics and relativity. In
AQFT, quantum mechanics is modelled by C*-algebras of observables and relativity
is usually modelled in Minkowski space. In this thesis we will consider a generalization
of AQFT which was inspired by the work of Abramsky and Coecke on abstract
quantum mechanics [1, 2]. In their work, Abramsky and Coecke develop a categorical
framework that captures many of the essential features of finite-dimensional quantum
mechanics.
In our setting we develop a categorified version of AQFT, which we call premonoidal
C*-quantum field theory, and in the process we establish many analogues of
classical results from AQFT. Along the way we also exhibit a number of new concepts,
such as a von Neumann category, and prove several properties they possess.
We also establish some results that could lead to proving a premonoidal version
of the classical Doplicher-Roberts theorem, and conjecture a possible solution to constructing
a fibre-functor. Lastly we look at two variations on AQFT in which a causal
order on double cones in Minkowski space is considered.
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Sanders, Jacobus Ambrosius. "Aspects of locally covariant quantum field theory." Thesis, University of York, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490310.
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This thesis considers various aspects of locally covariant quantum field theory (see Brunetti et al., Commun. Math. Phys. 237 (2003), 31-68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes. Chapter 1 argues that the use of morphisms in this framework can be seen as a model for modal logic. To our knowledge this is the first interpretative description of this aspect of the framework. Chapter 2 gives an exposition of locally covariant quantum field theory which differs from the original in minor details, notably in the new notion of nowhere-classicality and the sharpened time-slice axiom, which puts a restriction on the state space as well as the algebras. Chapter 3 deals with the well-studied example of the free real scalar field and includes an elegant proof of the new general result that the commutation relations together with the Hadamard condition on the two-point distribution of a state completely fix the singularity structure of all n-point distributions. Chapter 4 describes the free Dirac field as a locally covariant quantum field, using a new representation independent approach, demonstrating that the physics is determined entirely by the relations between the adjoint map, charge conjugation and Dirac operator. It also proves the new result that the relative Cauchy evolution is related to the stress-energy-momentum tensor in the same way as for the free scalar field. Chapter 5 studies the Reeh-Schlieder property, both in the general setting and in specific examples. We obtain various interesting results concerning this property in curved spacetimes, most notably by using the idea of spacetime deformation, but some open questions and opportunities for further research remain. We will freely make use of smooth and analytic wave front sets throughout. These concepts are explained in appendix A, using a new and elegant way to generalise results for scalar distributions to Banach space-valued distributions, leading to some new but expected results.
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Mitchard, Mark Gavin. "Non-perturbative methods in quantum field theory." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315867.
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Bedingham, Daniel John. "Quantum field theory and Bose Einstein condensation." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249588.
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Kjaergaard, Lars. "Analyticity and scaling in quantum field theory." Thesis, Durham University, 2000. http://etheses.dur.ac.uk/4249/.
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The theory describing the scaling properties of quantum field theory is introduced. The symmetry principles behind scale and conformal transformations are reviewed together with the renormalisation group. A method for improving perturbative calculations of physical quantities in the infra-red limit is developed using general analyticity properties valid for all unitary quantum field theories. The infra-red limit of a physical quantity is shown to equal the limiting value of the Borel transform in a complex scale parameter, where the order of the Borel transform is related to the domain of analyticity. It is shown how this general result can be used to improve perturbative calculations in the infra-red limit. First, the infra-red central charge of a perturbed conformal field theory is considered, and for the unitary minimal models perturbed by ɸ(1,3) the developed approximation is shown to be very close to the exact results by improving only a one loop perturbation. The other example is the infra-red limit of the critical exponents of x(^4) theory in three dimensions, where our approximation is within the limits of other approximations. The exact renormalisation group equation is studied for a theory with exponential interactions and a background charge. It is shown how to incorporate the background charge, and using the operator product expansion together with the equivalence between the quantum group restricted sine-Gordon model and the unitary minimal models perturbed by ɸ(1,3), the equation obtained is argued to describe the flow between unitary minimal models. Finally, a semi-classical approximation of the low energy limit of a bosonic membrane is studied where the action is taken to be the world-volume together with an Einstein-Hilbert term. A solution to the linearized equations of motion is determined describing a membrane oscillating around a flat torus.
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Ali, David Benedict. "Aspects of non-Abelian quantum field theory." Thesis, University of Liverpool, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368626.
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Yang, Ting-Cheng. "Aspects of gravity in quantum field theory." Thesis, University of Sussex, 2014. http://sro.sussex.ac.uk/id/eprint/50763/.
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This thesis studies three aspects of gravity in quantum field theory. First quantum gravity effects are investigated using effective field theory techniques. In particular, we consider quantum gravity effects in grand unified theory and study their effects on the unification of the masses in such models. We find that the fermion masses unification conditions receive a sizeable correction from the quantum gravitational effects and one thus cannot predict the high energy unification only by the extrapolation from low energy physics without the understanding of gravitational effect in high energy. Secondly we study quantum field theory in curved spacetime in order to understand further about some of the properties of gravity. Keeping gravity as background field we discuss modified gravity theories in different set of parameters called frames; they are the Jordan frame and the Einstein frame respectively. We show how to map gravitational theories at the quantum field theoretical level. The key observation is that there is a non-trivial Jacobian. It can be interpreted as boundary term. Finally we investigate a new canonical quantisation paradigm. In that framework, quantum gravity is power counting renormalisable. Furthermore, the theory is unitary and the problem of time is solved. We use this framework to calculate the solution for the quantum wave function and the semiclassical Hamilton-Jacob function. We study the Hawking-Bekenstein entropy in the spherical symmetric mini-superspace for Schwarzschild black hole, and find that it can be produced naturally from first principles. Importantly it is accompanied naturally by non-thermal quantum correction terms which is generally believed to restore the information loss.
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Monoyios, Michael. "New perturbation expansions for quantum field theory." Thesis, Imperial College London, 1989. http://hdl.handle.net/10044/1/47573.
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Tassev, Svetlin Valentinov. "Quantum field theory of scalar cosmological perturbations." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32906.
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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.<br>Includes bibliographical references (leaf 55).<br>Using canonical quantization we show that the spectrum of the scalar cosmological fluctuations as calculated until now is not correct. We derive the correct expression for the spectrum, and show that our correct treatment alleviates the fine-tuning problem in inflation.<br>by Svetlin Valentinov Tassev.<br>S.B.
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Jizba, Petr. "Equilibrium and non-equilibrium quantum field theory." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624406.
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Eyink, Gregory Lawrence. "Quantum field-theory in non-integer dimensions /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487584612164091.
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Collini, Giovanni. "Fedosov Quantization and Perturbative Quantum Field Theory." Doctoral thesis, Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-224698.
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Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold (\\\"phase space\\\"). His algorithm gives a non-commutative, but associative, product (a so-called \\\"star-product\\\") between smooth phase space functions parameterized by Planck\\\'s constant ℏ, which is treated as a deformation parameter. In the limit as ℏ goes to zero, the star product commutator goes to ℏ times the Poisson bracket, so in this sense his method provides a quantization of the algebra of classical observables. In this work, we develop a generalization of Fedosov\\\'s method which applies to the infinite-dimensional symplectic \\\"manifolds\\\" that occur in Lagrangian field theories. We show that the procedure remains mathematically well-defined, and we explain the relationship of this method to more standard perturbative quantization schemes in quantum field theory.
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Teresi, Daniele. "Quantum field theory for the early universe." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/quantum-field-theory-for-the-early-universe(050a2a86-9302-4c2d-81da-53f2fb47492a).html.
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In this thesis we discuss the quantum field-theoretical techniques that allow a consistent, complete and unified description of the generation of the observed matter/antimatter asymmetry in the Early Universe, through the Resonant Leptogenesis mechanism. After reviewing the basic formalism of thermal field theory at equilibrium, we present the paradigm of leptogenesis, with particular emphasis on the resonant case, in which the presence of quasi-degenerate heavy Majorana neutrinos can enhance significantly the CP asymmetry generated by their decays in the Early Universe. After these introductory discussions, we develop a fully flavour-covariant formalism for transport phenomena, capable of describing the time-evolution of particle number-densities in a statistical ensemble with arbitrary flavour content. By using this formalism for a semi-classical analysis of Resonant Leptogenesis, in which the resummation of resonant heavy-neutrino absorptive transitions is performed effectively at zero temperature, we obtain the flavour-covariant rate equations, that provide a complete and unified description of this phenomenon, capturing three relevant physical effects: (i) the resonant mixing between the heavy-neutrino states, (ii) coherent oscillations between heavy-neutrino flavours, and (iii) quantum decoherence effects in the charged-lepton sector. Subsequently, we discuss the consistent field-theoretical formulation of non-equilibrium phenomena and use it to develop a flavour-covariant analysis of Resonant Leptogenesis in a fully thermal-field-theoretical framework. This formalism allows us to confirm the results of the semi-classical analysis in a more first-principles approach, and provides the consistent thermal description of the resonant enhancement of the asymmetry due to heavy-neutrino mixing. Finally, we present an explicit model of Resonant Leptogenesis, with electroweak-scale Majorana neutrinos and observable signatures in current and near-future experiments. We study the predictions of this model by means of the flavour-covariant rate equations, and demonstrate the numerical significance of the formalism developed in this thesis for an accurate prediction of the baryon asymmetry generated in the Early Universe.
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Casali, Eduardo. "Worldsheet methods for perturbative quantum field theory." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/265833.
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This thesis is divided into two parts. The first part concerns the study of the ambitwistor string and the scattering equations, while the second concerns the interplay of the symmetries of the asymptotic null boundary of Minkowski space, called [scri], and scattering amplitudes. The first part begins with a review of the CHY formulas for scattering amplitudes, the scattering equations and the ambitwistor string including its pure spinor version. Next are the results of this thesis concerning these topics, they are: generalizing the ambitwistor model to higher genus surfaces; calculating the one-loop NS-NS scattering amplitudes and studying their modular and factorization properties; deriving the one-loop scattering equations and analyzing their factorization; showing that, in the case of the four graviton amplitude, the ambitwistor amplitude gives the expected kinematical prefactor; matching this amplitude to the field theory expectation in a particular kinematical regime; solving the one loop scattering equations in this kinematical regime; a conjecture for the IR behaviour of the one-loop ambitwistor integrand; computing the four graviton, two-loop amplitude using pure spinors; showing that this two-loop amplitude has the correct kinematical prefactor and factorizes as expected for a field theory amplitude; generalizing the ambitwistor string to curved backgrounds; obtaining the field equations for type II supergravity as anomaly cancellation on the worldsheet; generalizing the scattering equations for curved backgrounds. The second part begins with a review of the definition of the null asymptotic boundary of four dimensional Minkowski space, its symmetry algebra, and their relation to soft particles in the S-matrix. Next are the results of this thesis concerning these topics, they are: constructing two models consisting of maps from a worldsheet to [scri], one containing the spectrum of N=8 supergravity, and the other the spectrum of N=4 super Yang-Mills; showing how certain correlators in these theories calculate the tree-level S-matrix of N=8 sugra and N=4 sYM respectively; defining worldsheet charges which encode the action of the appropriate asymptotic symmetry algebra and showing that their Ward-identities recover the soft graviton, and soft gluon factors; defining worldsheet charges for proposed extensions of these symmetry algebras and showing that their Ward-identities give the subleading soft graviton and subleading soft gluon factors.
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Gargiulo, Maria Vittoria. "On neutrino mixing in Quantum Field Theory." Doctoral thesis, Universita degli studi di Salerno, 2017. http://hdl.handle.net/10556/2606.
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2015 - 2016<br>Neutrino physics is one of the most important areas in research on the fundamental interactions, both theoretically and experimentally. A central issue in the study of these particles is related to the properties of mixing and flavor oscillations. In particular, a necessary condition for the mixing is that neutrinos have mass, a feature which is not considered by the Standard Model, and which poses the problem of the origin and nature of these masses. The theoretical basis of neutrino mixing has been studied in many details and in the late ’90 a quantum field theory (QFT) formalism for mixed fields has been developed thanks to which it was found that mixing transformations induce a condensed structure in the flavour vacum with possible phenomenological consequences. In particular, the usual formulas of Pontecorvo oscillation are arising as the relativistic limit of exact formulas in the context of field theory. Within this framework it is inserted our work, finalized to the study of algebraic properties of the mixing transformations generator in QFT and its components. In quantum mechanics (QM) the mixing transformation looks like a rotation operating on massive neutrino states. We show explicitly that such a rotation is not sufficient for implementing the mixing transformation at level of fields. It is necessary, in fact, also the action of a Bogoliubov transformation which operates a suitable mass shift. Such a property of Bogoliubov transformations has been already known and used since long time, e.g. in renormalization theory or in the dynamical generation of mass. We then analyze the condensate nature of the flavor vacuum and the roˆle played by the non commutativity between the rotation and the Bogoliubov transformation. This structure of the vacuum also suggests a thermodynamical interpretation which we investigate, showing peculiarities in the thermal behavior due to
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the character of the particle-antiparticle condensate involved in the flavor vacuum. The key point in our analysis is the non commutativity between rotation and Bogoliubov transformations, a feature which turns out to be at the origin of the inequivalence among mass and flavor vacua. From another point of view, the Bogoliubov transformation are shown to naturally arise when studying the neutrino mixing in the contest of the Noncommutative Spectral Geometry in Alain Connes’ construction and the algebra doubling he introduces. Given the algebraic nature of our arguments, we have good reasons to believe that the results we have obtained are general and also extend to the mixing phenomenon of any particle, even if our analysis is limited to the case of two Dirac neutrinos.
Thethesisisstructuredasfollows: afteranIntroduction tothearguments of our work is presented; in Chapter 1 we briefly summarise the main aspects of the Standard Model and of neutrino mixing. Chapter 2 is dedicated to neutrino mixing and oscillations, considering both the quantum mechanics approach and the quantum field theory formalism. In Chapter 3 we analyze the mixing generator, decomposing it into components, and the flavor vacuum structure, studying its thermodynamical properties. A noncommutative structure will arise. Chapter 4 is focused non commutativity, giving some known examples of noncommutative systems, and briefly presenting noncommutative geometry and noncommutative spectral geometry (NCSG) elements. In Chapter 5 we introduce further notions on Alain Connes’ construction; we summarize how neutrinos appear within this construction and werelatethealgebradoubling,whichisacrucialelementoftheNCSGmodel, totheHopfnon-commutativealgebraandBogoliubovtransformations,which play a key role in the neutrino mixing. In Chapter 6, in order to better understand the mixing phenomenon, we study a classical system analogue for it. We then close with our Conclusions and Outlook.
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The results obtained and presented in this thesis have been published in the following international journals: • M.V. Gargiulo, M. Sakellariadou, G.Vitiello, Doubling of the Algebra and Neutrino Mixing within Noncommutative Spectral Geometry, EPJ C (2014) 74 2695 ; • M.V. Gargiulo, M. Sakellariadou, G.Vitiello, Noncommutativespectralgeometry, Bogoliubovtransformationsandneutrino oscillations, Journal of Physics: Conference Series (2015) 626 012014 ; • M.Blasone, M.V.Gargiulo and G.Vitiello, Disentangling mass and angle dependence in neutrino mixing, Journal of Physics: Conference Series (2015) 626 012026 ; • M. Blasone, M.V. Gargiulo, G. Vitiello, On the role of rotations and Bogoliubov transformations in neutrino mixing, Phys. Lett. B (2016) 761 104; • M.Blasone, M.V. Gargiulo, G.Vitiello, Semiclassical aspect of neutrino mixing Journal of Physics: Conference Series (2017), in press.
Work in progress • M.Blasone, M.V. Gargiulo, G.Vitiello, Noncommutative aspects of neutrino mixing, work in progress. [edited by author]<br>XXIX n.s.
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Runkel, Ingo. "Boundary problems in conformal field theory." Thesis, King's College London (University of London), 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326066.
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Rosaler, Joshua S. "Inter-theory relations in physics : case studies from quantum mechanics and quantum field theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:1fc6c67d-8c8e-4e92-a9ee-41eeae80e145.
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I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level (purportedly more accurate and encompassing) model to that of the high-level (purportedly less accurate and encompassing) model that approximately commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity.
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Roberts, Justin Deritter. "Quantum invariants via skein theory." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319336.
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Calderon, Hector Hugo. "Applications of quantum field theory in curved spacetimes." Diss., Montana State University, 2007. http://etd.lib.montana.edu/etd/2007/calderon/CalderonH1207.pdf.
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Gill, Alasdair James. "Field theory and topological defects." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244675.
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Gómez, Valent Adrià. "Vacuum Energy in Quantum Field Theory and Cosmology." Doctoral thesis, Universitat de Barcelona, 2017. http://hdl.handle.net/10803/459249.
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The cosmological constant appearing in Einstein’s equations is a key element of the ΛCDM standard cosmological model. This term performs, effectively, as pure vacuum energy, and is considered the easiest explanation of the positive acceleration of the current Universe. But despite the successes of the concordance model in explaining a large variety of high precision data, some tensions are also present at the observational level, and there are also some important problems arising on the theoretical side. The most severe one is the so-called “cosmological constant problem”, which is caused by the gigantic discrepancy between the predicted value of the vacuum energy density in Quantum Field Theory and the measured one. This huge difference is considered as one of the most profound (unsolved) problems of theoretical Physics and its solution probably will come hand in hand with a change of paradigm. But at this moment, there is no clear hint pointing to the aforesaid solution. In view of the current status of the problem, those phenomenological studies that are able to shed some light on the nature of the dark energy (DE) component that is dominating the current Universe, are very welcome.
In this thesis are presented detailed studies (at the background and perturbations levels) on various running vacuum energy models, which are motivated from the renormalization group equation formalism of Quantum Field Theory in curved spacetime. In these models, the cosmological term is not a rigid Λ, it depends explicitly on the Hubble function and its time derivative. Thus, it varies with the cosmic expansion. Upon the study of the capability of these models on fitting the experimental data, we can determine whether this dynamical behavior is favored by observations or not. Is the vacuum energy density (or in more general terms, the dark energy density) dynamical? One of the main conclusions of this dissertation is that we have indeed strong evidences in favor of the variability of the DE throughout the cosmic history. It has been shown that this variation can also be traced through other (purely phenomenological) dynamical vacuum models, together with different parameterizations of the DE (as the XCDM and CPL), and scalar field models as the Peebles-Ratra one. The statistical confidence level with which these evidences are obtained reaches in some cases the 4σ c.l., something that is unprecedented in the literature. An exhaustive explanation on the reasons why large collaborations as BOSS or Planck have not been able to detect such signal in favor of the DE dynamics is provided in this thesis too. This is mainly due to the fact that they do not make use of a complete enough data set that include more large scale structure (LSS) and baryon acoustic oscillations (BAO’s) data points.
The analyses carried out in this thesis have also served e.g. for: 1) ruling out some running vacuum models (and DE models inside the D-class) without a well-defined ΛCDM limit (with no constant term in the expression for the vacuum energy density); 2) showing the potential of the Press-Schechter formalism in the characterization of the various vacuum models; 3) pinpointing the importance of the data set BAO+CMB+LSS in front of other data sets as those formed by Hubble function data points and the luminosity distance versus redshift points of type Ia supernovae.<br>La constant cosmològica és un element clau del model ΛCDM, el model estàndard cosmològic. Aquest terme actua, de manera efectiva, com energia pura de buit, i representa l’explicació més senzilla de l’acceleració positiva amb la que s’expandeix l’Univers actualment. Ara bé, tot i que el model estàndard cosmològic és capaç de desciure dades observacionals provinents de fonts molt diverses amb molta precisió, es coneixen també algunes tensions a nivell observacional, així com també greus problemes teòrics associats. El més sever és el que es coneix com el “problema de la constant cosmològica” i té a veure amb la gran diferència (de més de 55 ordres de magnitud) entre l’estimació teòrica de la densitat d’energia de buit que es fa a partir de la Teoria Quàntica de Camps i el valor mesurat de la mateixa. Aquesta discrepància és exageradament gran i representa un dels problemes més importants de la Física teòrica actual. Ara per ara, no sembla que disposem de les eines teòriques per solucionar aquest problema. En aquest sentit, estudis fenomenològics que puguin ajudar a caracteritzar millor l’energia fosca que domina l’expansió del teixit còsmic són molt benvinguts.
En aquesta tesi es recullen els estudis detallats (a nivell de background i pertorbacions) de diferents models de buit dinàmic que neixen del formalisme del grup de renormalització en Teoria Quàntica de Camps en espais corbats. En aquests models, el terme cosmològic no es pren constant, sinó com una funció explítica de la funció de Hubble i la seva derivada. Per tant, la densitat d’energia de buit varia amb l’expansió de l’Univers. Estudiant la capacitat d’aquests models per ajustar les dades experimentals podem veure si realment la dinàmica d’aquesta component còsmica està o no afavorida per les observacions. És la densitat d’energia de buit (o, en termes més generals, la densitat d’energia fosca) dinàmica? Una de les conclusions més importants a les que s’arriba en aquesta dissertació és que hi ha indicis grans a favor d’aquesta variabilitat de l’energia fosca en el temps i que aquesta pot ser traçada també a partir d’altres models de buit dinàmic purament fenomenològics, així com amb diverses parametritzacions de l’energia fosca (com la XCDM o CPL) i models de camps escalars com el de Peebles- Ratra. El nivell trobat d’evidència a favor d’aquesta dinàmica no nul·la no té precedents a la literatura, arribant en alguns casos a les 4σ de nivell de confiança.
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Sprague, Kevin B. "Investigations and techniques in nonperturbative quantum field theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0004/NQ42553.pdf.
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Archer, Francis John. "A simplicial approach to topological quantum field theory." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260593.
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