Rozprawy doktorskie na temat „Quantum field theory”

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.

2009 - 2010
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]
IX n.s.

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.

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.

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.
Physics

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.

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.

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.

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.

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.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.
Includes bibliographical references (leaf 55).
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.
by Svetlin Valentinov Tassev.
S.B.

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.

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.

2015 - 2016
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 2 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. 3 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]
XXIX n.s.

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.