Relevant bibliographies by topics / Algebraic quantum theory

Academic literature on the topic 'Algebraic quantum theory'

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Published: 11 March 2023

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Journal articles on the topic "Algebraic quantum theory"

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Ellis, Eugenia. "Algebraic quantum kk-theory." Communications in Algebra 46, no. 8 (February 8, 2018): 3642–62. http://dx.doi.org/10.1080/00927872.2018.1424877.

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KITAJIMA, Yuichiro. "Contextuality in Algebraic Quantum Theory." Journal of the Japan Association for Philosophy of Science 45, no. 1-2 (2018): 23–34. http://dx.doi.org/10.4288/kisoron.45.1-2_23.

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Petz, Dénes. "Algebraic complementarity in quantum theory." Journal of Mathematical Physics 51, no. 1 (January 2010): 015215. http://dx.doi.org/10.1063/1.3276681.

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Kravzova, G. A. "Algebraic quantum theory with maximal frequency." Theoretical and Mathematical Physics 208, no. 2 (August 2021): 1051–60. http://dx.doi.org/10.1134/s0040577921080055.

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Heunen, Chris, Nicolaas P. Landsman, and Bas Spitters. "A Topos for Algebraic Quantum Theory." Communications in Mathematical Physics 291, no. 1 (July 21, 2009): 63–110. http://dx.doi.org/10.1007/s00220-009-0865-6.

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Green, H. S. "Quantum Theory of Gravitation." Australian Journal of Physics 51, no. 3 (1998): 459. http://dx.doi.org/10.1071/p97084.

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It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles. Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation. From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry. The algebraic method is extended to obtain solutions of Einstein’s gravitational field equations for empty space, with a cosmological term. General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein"s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) ⊗ SO(4; 2). There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation.
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Timmermann, Thomas. "Integration on algebraic quantum groupoids." International Journal of Mathematics 27, no. 02 (February 2016): 1650014. http://dx.doi.org/10.1142/s0129167x16500142.

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In this paper, we develop a theory of integration on algebraic quantum groupoids in the form of regular multiplier Hopf algebroids, and establish the main properties of integrals obtained by Van Daele for algebraic quantum groups before — faithfulness, uniqueness up to scaling, existence of a modular element and existence of a modular automorphism — for algebraic quantum groupoids under reasonable assumptions. The approach to integration developed in this paper forms the basis for the extension of Pontrjagin duality to algebraic quantum groupoids, and for the passage from algebraic quantum groupoids to operator-algebraic completions, which both will be studied in separate papers.
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BENINI, MARCO, CLAUDIO DAPPIAGGI, and THOMAS-PAUL HACK. "QUANTUM FIELD THEORY ON CURVED BACKGROUNDS — A PRIMER." International Journal of Modern Physics A 28, no. 17 (July 10, 2013): 1330023. http://dx.doi.org/10.1142/s0217751x13300238.

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Goal of this paper is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, it is assigned to a physical system a suitable algebra of observables, which is meant to encode all algebraic relations among observables, such as commutation relations. In the second step, one must select an algebraic state in order to recover the standard Hilbert space interpretation of a quantum system. As quantum field theories possess infinitely many degrees of freedom, many unitarily inequivalent Hilbert space representations exist and the power of such approach is the ability to treat them all in a coherent manner. We will discuss in detail the algebraic approach for free fields in order to give the reader all necessary information to deal with the recent literature, which focuses on the applications to specific problems, mostly in cosmology.
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Plotnitsky, Arkady. "“The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory." Entropy 20, no. 9 (August 30, 2018): 656. http://dx.doi.org/10.3390/e20090656.

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The article reconsiders quantum theory in terms of the following principle, which can be symbolically represented as QUANTUMNESS → PROBABILITY → ALGEBRA and will be referred to as the QPA principle. The principle states that the quantumness of physical phenomena, that is, the specific character of physical phenomena known as quantum, implies that our predictions concerning them are irreducibly probabilistic, even in dealing with quantum phenomena resulting from the elementary individual quantum behavior (such as that of elementary particles), which in turn implies that our theories concerning these phenomena are fundamentally algebraic, in contrast to more geometrical classical or relativistic theories, although these theories, too, have an algebraic component to them. It follows that one needs to find an algebraic scheme able make these predictions in a given quantum regime. Heisenberg was first to accomplish this in the case of quantum mechanics, as matrix mechanics, whose matrix character testified to his algebraic method, as Einstein characterized it. The article explores the implications of the Heisenberg method and of the QPA principle for quantum theory, and for the relationships between mathematics and physics there, from a nonrealist or, in terms of this article, “reality-without-realism” or RWR perspective, defining the RWR principle, thus joined to the QPA principle.
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Schwarz, A. "Geometric and algebraic approaches to quantum theory." Nuclear Physics B 973 (December 2021): 115601. http://dx.doi.org/10.1016/j.nuclphysb.2021.115601.

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Dissertations / Theses on the topic "Algebraic quantum theory"

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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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Hart, A. C. D. "An algebraic approach to bound state quantum field theory." Thesis, University of Nottingham, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233666.

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Alcántara, Bode Julio, and J. Yngvason. "Algebraic quantum field theory and noncommutative moment problems I." Pontificia Universidad Católica del Perú, 2013. http://repositorio.pucp.edu.pe/index/handle/123456789/96072.

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Lang, Benjamin. "Universal constructions in algebraic and locally covariant quantum field theory." Thesis, University of York, 2014. http://etheses.whiterose.ac.uk/8019/.

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The present work is concerned with the application of categorical methods in algebraic and locally covariant quantum field theory. Attention is particularly paid to colimits and left Kan extensions, understanding K. Fredenhagen’s universal algebra, which is a global (unital) (C)*-algebra associated with a not necessarily up-directed net of local (unital) (C)*-algebras, from the point of view of category theory. The main technical result centres on explicit expressions for the universal algebra and its non-triviality in the case that a net of local unital *-algebras is constructed from linear symplectic spaces via a functorial quantisation prescription. Non-up-directed nets of local (unital) (C)*-algebras typically arise for quantum field theories in a generic curved spacetime with an arbitrary topology. As an example the field strength tensor description of the classical and the quantised free Maxwell field in curved spacetimes is considered. Employing colimits and left Kan extensions, a universal classical and quantum field theory are constructed. Both fail local covariance and dynamical locality but can be reduced to locally covariant and dynamically local theories. To understand C.J. Isham’s twisted quantum fields from the point of view of algebraic and locally covariant quantum field theory, an abstract categorical framework is introduced, which utilises recent ideas of C.J. Fewster on the automorphisms of a locally covariant theory and the group of the global gauge transformations of a theory. The general formalism allows to consider twisted variants of generic locally covariant theories, which need not refer to (quantum) fields at all, on single curved spacetimes. It is argued that the general categorical scheme leads naturally to the classification of the twisted variants of a locally covariant theory by the isomorphism classes of flat smooth principal bundles over the fixed single curved spacetime the twisted variants are considered on. The general categorical scheme and the classification of twisted variants are illustrated by the example of twisted variants of multiple free and minimally coupled real scalar fields of the same mass. Finally, a new family of pure and quasifree states for the quantised free massive Dirac field on 4-dimensional, oriented and globally hyperbolic ultrastatic slabs with compact spatial section is constructed, arising from a recent description of F. Finster’s fermionic projector. These FP-states (“FP” for fermionic projector) are tested for the Hadamard property with some negative and some positive results.
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Nyman, Adam. "The geometry of points on quantum projectivizations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/5727.

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Cooney, Nicholas. "Quantum multiplicative hypertoric varieties and localization." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:17d0824f-e8f2-4cb7-9e84-dd3850a9e2a2.

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In this thesis, we consider q-deformations of multiplicative Hypertoric varieties, where q∈𝕂x for 𝕂 an algebraically closed field of characteristic 0. We construct an algebra Dq of q-difference operators as a Heisenberg double in a braided monoidal category. We then focus on the case where q is specialized to a root of unity. In this setting, we use Dq to construct an Azumaya algebra on an l-twist of the multiplicative Hypertoric variety, before showing that this algebra splits over the fibers of both the moment and resolution maps. Finally, we sketch a derived localization theorem for these Azumaya algebras.
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Lu, Weiyun. "Topics in Many-valued and Quantum Algebraic Logic." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35173.

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Introduced by C.C. Chang in the 1950s, MV algebras are to many-valued (Łukasiewicz) logics what boolean algebras are to two-valued logic. More recently, effect algebras were introduced by physicists to describe quantum logic. In this thesis, we begin by investigating how these two structures, introduced decades apart for wildly different reasons, are intimately related in a mathematically precise way. We survey some connections between MV/effect algebras and more traditional algebraic structures. Then, we look at the categorical structure of effect algebras in depth, and in particular see how the partiality of their operations cause things to be vastly more complicated than their totally defined classical analogues. In the final chapter, we discuss coordinatization of MV algebras and prove some new theorems and construct some new concrete examples, connecting these structures up (requiring a detour through effect algebras!) to boolean inverse semigroups.
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Solanki, Vinesh. "Zariski structures in noncommutative algebraic geometry and representation theory." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45.

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A suitable subcategory of affine Azumaya algebras is defined and a functor from this category to the category of Zariski structures is constructed. The rudiments of a theory of presheaves of topological structures is developed and applied to construct examples of structures at a generic parameter. The category of equivariant algebras is defined and a first-order theory is associated to each object. For those theories satisfying a certain technical condition, uncountable categoricity and quantifier elimination results are established. Models are shown to be Zariski structures and a functor from the category of equivariant algebras to Zariski structures is constructed. The two functors obtained in the thesis are shown to agree on a nontrivial class of algebras.
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BRAGA, DE GOES E. VASCONCELLOS JOAO. "Thermal equilibrium states in perturbative Algebraic Quantum Field Theory in relation to Thermal Field Theory." Doctoral thesis, Università degli studi di Genova, 2019. http://hdl.handle.net/11567/979745.

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In the first part, we analyse the properties of an interacting, massive scalar field in an equilibrium state over Minkowski spacetime. We compare the known real- and imaginary-time formalisms of Thermal Field Theory with the recent construction by Fredenhagen and Lindner of a KMS state for perturbative interacting theories in the context of perturbative Algebraic Quantum Field Theory, in the adiabatic limit. In particular, we show that the construction of Fredenhagen and Lindner reduces to the real-time formalism only if the cocycle which intertwines between the free and interacting dynamics can be neglected. Furthermore, the Fredenhagen and Lindner construction reduces to the ordinary imaginary-time formalism if one considers the expectation value of translation invariant observables. We thus conclude that a complete description of thermal equilibrium for interacting scalar fields is generally obtained only by means of the state constructed by Fredenhagen and Lindner, which combines both formalisms of Thermal Field Theory. We also discuss the properties of the expansion of the Fredenhagen and Lindner construction in terms of Feynman diagrams in the adiabatic limit. We finally provide examples showing that the real- and the imaginary-time formalisms fail to describe thermal equilibrium already at first or second order in perturbation theory. The results presented in this part are summarized in (BDP19). In the second part, we discuss the so-called secular effects, characterized by the appearance of polynomial divergences in the large time limit of truncated perturbative expansions of expectation values in Quantum Field Theory. We show that, although such effect is an artifact of perturbation theory, and thus may not be obtained via exactly solving the dynamical equation if possible, they do not represent the breakdown of perturbation theory itself. Instead, we show that the polynomial divergences follow from a bad choice of state, and we present examples of states which produce expectation values whose perturbative expansion does not present secular effects. In particular, we point that it is possible to obtain non time-divergent perturbative expressions from thermal equilibrium states for the interacting theory. This last part is based on a research project which, by the time this thesis was written, had not been concluded yet.
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FALDINO, FEDERICO MARIA. "Facets of Non-Equilibrium in Perturbative Quantum Field Theory : an Algebraic Approach." Doctoral thesis, Università degli studi di Genova, 2018. http://hdl.handle.net/11567/933558.

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In this thesis we study some non-equilibrium aspects of an interacting, massive scalar field theory treated perturbatively. This is done analysing some properties of the interacting KMS state constructed by Fredenhagen and Lindner [FL14] in the framework of perturbative Algebraic Quantum Field Theory. In the first part we treat the stability of KMS states, namely we check whether the free state evolved with the interacting dynamics converges to the interacting state. In the meantime we also analyse the return to equilibrium, that is the analogous property with the role of the free and interacting quantities exchanged. We prove that those two properties hold if the perturbation potential is of spatial compact support and that they fail otherwise, even if an adiabatic mean is considered. While the stability leads to non-curable divergencies, the analysis of return to equilibrium gives something finite, which is interpreted as a non-equilibrium steady state. The novelty of this non-equilibrium state drove us to try to characterise it in more details. To do so, in the second part we introduce relative entropy and entropy production for perturbative quantum field theory, justifying those definitions by proving their main properties. Furthermore, we showed that they are well-defined in the adiabatic limit if we consider densities. These two definitions allowed to prove that the non-equilibrium steady state is thermodynamically trivial, namely it has zero entropy production. The present thesis is based on [DFP18a, DFP18b].
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Books on the topic "Algebraic quantum theory"

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Rejzner, Kasia. Perturbative Algebraic Quantum Field Theory. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-25901-7.

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Khoruzhiĭ, S. S. Introduction to algebraic quantum field theory. Dordrecht, Netherlands: Kluwer Academic Publishers, 1990.

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Brunetti, Romeo, Claudio Dappiaggi, Klaus Fredenhagen, and Jakob Yngvason, eds. Advances in Algebraic Quantum Field Theory. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21353-8.

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Horuzhy, S. S. Introduction to Algebraic Quantum Field Theory. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-1179-6.

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Apagyi, Barnabás, Gábor Endrédi, and Péter Lévay, eds. Inverse and Algebraic Quantum Scattering Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0104919.

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Apagyi, Barnabás, Gábor Endrédi, and Péter Lévay, eds. Inverse and Algebraic Quantum Scattering Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-14145-8.

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Khoruzhiĭ, S. S. Introduction to Algebraic Quantum Field Theory. Dordrecht: Springer Netherlands, 1989.

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Rédei, Miklós. Quantum logic in algebraic approach. Dordrecht: Kluwer Academic Publishers, 1998.

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Ozawa, Masanao, Jeremy Butterfield, Hans Halvorson, Miklós Rédei, Yuichiro Kitajima, and Francesco Buscemi, eds. Reality and Measurement in Algebraic Quantum Theory. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2487-1.

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Ezra, Segal Irving, and Zhou Zhengfang 1959-, eds. Introduction to algebraic and constructive quantum field theory. Princeton, N.J: Princeton University Press, 1992.

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Book chapters on the topic "Algebraic quantum theory"

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Bongaarts, Peter. "Physical Theories as Algebraic Systems." In Quantum Theory, 171–86. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09561-5_12.

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Fewster, Christopher J., and Kasia Rejzner. "Algebraic Quantum Field Theory." In Progress and Visions in Quantum Theory in View of Gravity, 1–61. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38941-3_1.

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Bru, J. B., and W. de Siqueira Pedra. "Algebraic Quantum Mechanics." In Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory, 5–15. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45784-0_2.

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Becchi, Carlo, Stefano Giusto, and Camillo Imbimbo. "The Algebraic Method in Renormalization Theory." In Quantum Field Theory, 15–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44482-3_2.

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Patrascu, Andrei-Tudor. "Algebraic Topology." In The Universal Coefficient Theorem and Quantum Field Theory, 31–38. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-46143-4_3.

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Rejzner, Kasia. "Algebraic Approach to Quantum Theory." In Perturbative Algebraic Quantum Field Theory, 3–37. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-25901-7_2.

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Hudson, R. L. "Algebraic theory of quantum diffusions." In Lecture Notes in Mathematics, 113–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0077920.

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Fredenhagen, Klaus, and Katarzyna Rejzner. "Perturbative Algebraic Quantum Field Theory." In Mathematical Physics Studies, 17–55. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-09949-1_2.

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Landsman, Klaas. "Symmetry in algebraic quantum theory." In Fundamental Theories of Physics, 333–66. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51777-3_9.

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Adams, Barry G. "Lie Algebraic Perturbation Theory." In Algebraic Approach to Simple Quantum Systems, 119–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57933-2_7.

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Conference papers on the topic "Algebraic quantum theory"

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Bohm, D. J. "Algebraic Quantum Mechanics and Pregeometry." In QUANTUM THEORY: Reconsideration of Foundations - 3. AIP, 2006. http://dx.doi.org/10.1063/1.2158735.

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Broadhurst, David, and Anton Mellit. "Perturbative quantum field theory informs algebraic geometry." In Loops and Legs in Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.260.0079.

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Broadhurst, David. "Algebraic geometry informs perturbative quantum field theory." In Loops and Legs in Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.211.0078.

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Hiley, B. J. "Quantum Space-Times: An Introduction to “Algebraic Quantum Mechanics and Pregeometry”." In QUANTUM THEORY: Reconsideration of Foundations - 3. AIP, 2006. http://dx.doi.org/10.1063/1.2158734.

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Khrennikov, A. Yu, and V. M. Maximov. "About some probabilistic algebraic model of interaction between particles." In ADVANCES IN QUANTUM THEORY: Proceedings of the International Conference on Advances in Quantum Theory. AIP, 2011. http://dx.doi.org/10.1063/1.3567468.

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Yang, Li, Lei Hu, and Deng-Guo Feng. "Quantum message authentication based on algebraic coding theory." In Photonics Asia 2004, edited by Guang-Can Guo, Hoi-Kwong Lo, Masahide Sasaki, and Songhao Liu. SPIE, 2005. http://dx.doi.org/10.1117/12.576777.

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Bertozzini, Paolo. "Categorical Operator Algebraic Foundations of Relational Quantum Theory." In Frontiers of Fundamental Physics 14. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.224.0206.

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van Dam, Wim, and Yoshitaka Sasaki. "QUANTUM ALGORITHMS FOR PROBLEMS IN NUMBER THEORY, ALGEBRAIC GEOMETRY, AND GROUP THEORY." In Summer School on Diversities in Quantum Computation/Information. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814425988_0003.

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Kocherova, A. S., and I. Yu Zhdanovskiy. "Some algebraic and geometric constructions in quantum information theory." In MIPT (PHYSTECH) - QUANT 2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0054917.

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Verma, Ram Krishna, Om Prakash, and Ashutosh Singh. "Quantum codes from skew constacyclic codes over Fp m + vFp m + v2Fp m." In 2020 Algebraic and Combinatorial Coding Theory (ACCT). IEEE, 2020. http://dx.doi.org/10.1109/acct51235.2020.9383402.

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