Готові списки джерел за темами / Quantum principal bundles

Добірка наукової літератури з теми "Quantum principal bundles"

Автор: Grafiati
Опубліковано: 14 березня 2023

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Статті в журналах з теми "Quantum principal bundles"

1

Đurđević, Mićo. "Geometry of Quantum Principal Bundles II." Reviews in Mathematical Physics 09, no. 05 (July 1997): 531–607. http://dx.doi.org/10.1142/s0129055x9700021x.

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A general non-commutative-geometric theory of principal bundles is developed. Quantum groups play the role of structure groups and general quantum spaces play the role of base manifolds. A general conceptual framework for the study of differential structures on quantum principal bundles is presented. Algebras of horizontal, verticalized and "horizontally vertically" decomposed differential forms on the bundle are introduced and investigated. Constructive approaches to differential calculi on quantum principal bundles are discussed. The formalism of connections is developed further. The corresponding operators of horizontal projection, covariant derivative and curvature are constructed and analyzed. In particular the analogs of the basic classical algebraic identities are derived. A quantum generalization of classical Weil's theory of characteristic classes is sketched. Quantum analogs of infinitesimal gauge transformations are studied. Interesting examples are presented.
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2

Aschieri, Paolo. "Deformation quantization of principal bundles." International Journal of Geometric Methods in Modern Physics 13, no. 08 (September 2016): 1630010. http://dx.doi.org/10.1142/s0219887816300105.

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We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles and, more in general, to the deformation of Hopf–Galois extensions. First, we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next, we twist deform a subgroup of the group of automorphisms of the principal bundle, and this leads to a noncommutative base space. Considering both deformations, we obtain noncommutative principal bundles with noncommutative fiber and base space as well.
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3

Brzeziński, Tomasz, and Simon A. Fairfax. "Bundles over Quantum RealWeighted Projective Spaces." Axioms 1, no. 2 (September 17, 2012): 201–25. http://dx.doi.org/10.3390/axioms1020201.

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The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that generalises the quantum disc, so do the constructed principal bundles. In the negative case the principal bundle is proven to be non-trivial and associated projective modules are described. In the positive case the principal bundles turn out to be trivial, and so all the associated modules are free. It is also shown that the circle (co)actions on the quantum Seifert manifold that define quantum real weighted projective spaces are almost free.
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4

Aschieri, Paolo, Rita Fioresi, and Emanuele Latini. "Quantum Principal Bundles on Projective Bases." Communications in Mathematical Physics 382, no. 3 (March 2021): 1691–724. http://dx.doi.org/10.1007/s00220-021-03985-4.

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AbstractThe purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum principal bundles over non affine bases. We study noncommutative principal bundles corresponding to $$G \rightarrow G/P$$ G → G / P , where G is a semisimple group and P a parabolic subgroup.
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5

Đurđević, Mićo. "Differential structures on quantum principal bundles." Reports on Mathematical Physics 41, no. 1 (February 1998): 91–115. http://dx.doi.org/10.1016/s0034-4877(98)80183-3.

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6

Brzeziński, Tomasz. "Translation map in quantum principal bundles." Journal of Geometry and Physics 20, no. 4 (November 1996): 349–70. http://dx.doi.org/10.1016/s0393-0440(96)00003-4.

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7

Hajac, Piotr M. "Strong connections on quantum principal bundles." Communications in Mathematical Physics 182, no. 3 (December 1996): 579–617. http://dx.doi.org/10.1007/bf02506418.

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8

Müller, Andreas. "Classifying spaces for quantum principal bundles." Communications in Mathematical Physics 149, no. 3 (October 1992): 495–512. http://dx.doi.org/10.1007/bf02096940.

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9

Durdević, Mićo. "Geometry of quantum principal bundles I." Communications in Mathematical Physics 175, no. 3 (February 1996): 457–520. http://dx.doi.org/10.1007/bf02099507.

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10

Budzyński, Robert J., and Witold Kondracki. "Quantum principal fibre bundles: Topological aspects." Reports on Mathematical Physics 37, no. 3 (June 1996): 365–85. http://dx.doi.org/10.1016/0034-4877(96)84074-2.

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Дисертації з теми "Quantum principal bundles"

1

Pagani, Chiara. "Quantum Principal Bundles and Instantons." Doctoral thesis, SISSA, 2005. http://hdl.handle.net/20.500.11767/4028.

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2

Zieliński, Bartosz. "Methods of constructing quantum principal bundles." Thesis, Swansea University, 2005. https://cronfa.swan.ac.uk/Record/cronfa42957.

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In this thesis two new methods of constructing non-commutative principal bundles or coalgebra Galois extensions are presented. The first method is based on the use of the cotensor product of coalgebra Galois extensions and can be seen as a generalization of the prolongation theory. Sufficient conditions for the cotensor product of quantum principal bundles (with strong connections) to give a new quantum principal bundle (with a strong connections) to give a new quantum principal bundle (with a strong connection) are derived. The second method uses the covering and gluing procedures developed by Calow and Matthes. The notion of a locally coalgebra Galois extension is introduced and conditions are derived for such an extension to be a (globally) coalgebra Galois extension. These constructions are illustrated by explicit examples based on non-commutative Hopf fibration. Also a new non-commutative Hopf fibration is presented, derived from the quantisation of a contact structure on the three-sphere.
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3

Zucca, Alessandro. "Dirac Operators on Quantum Principal G-Bundles." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4108.

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In this thesis I discuss some results on the noncommutative (spin) geometry of quantum principal G-bundles. The first part of the thesis is devoted to the study of spectral triples over toral bundles; extending some recent results by L. Dabrowski and A. Sitarz, we introduce the notion of projectable spectral triple for T^n-bundles. Moreover, we work out twisted Dirac operators. We discuss, in particular, the application of these results to noncommutative tori. In the second part of the thesis, instead, we work out a method for constructing real spectral triples over cleft quantum principal G-bundles and we study the properties of these triples and their behaviour under gauge transformations. Some of the results discussed in this thesis can also be found in the following papers: arXiv:1305.6185 arXiv:1308.4738
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Книги з теми "Quantum principal bundles"

1

Sontz, Stephen Bruce. Principal Bundles: The Quantum Case. Springer, 2015.

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2

Sontz, Stephen Bruce. Principal Bundles: The Quantum Case. Springer International Publishing AG, 2015.

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3

Sontz, Stephen Bruce. Principal Bundles: The Classical Case. Springer London, Limited, 2015.

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Частини книг з теми "Quantum principal bundles"

1

Sontz, Stephen Bruce. "Quantum Principal Bundles." In Universitext, 181–276. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15829-7_12.

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2

Beggs, Edwin J., and Shahn Majid. "Quantum Principal Bundles and Framings." In Grundlehren der mathematischen Wissenschaften, 385–484. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-30294-8_5.

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3

Kassel, Christian. "Quantum Principal Bundles up to Homotopy Equivalence." In The Legacy of Niels Henrik Abel, 737–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18908-1_25.

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4

Smolin, Lee. "On the Place of Qualia in a Relational Universe." In Consciousness and Quantum Mechanics, 482–514. Oxford University PressNew York, 2022. http://dx.doi.org/10.1093/oso/9780197501665.003.0018.

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Abstract We propose an approach to the question of how qualia fit into the physical world, in the context of a relational and realist completion of quantum theory, called the causal theory of views. This is a combination of an approach to a dynamics of discrete causal structures, called energetic causal sets, developed with M. Cortes, with a realist approach to quantum foundations, called the real ensemble formulation. In this theory, the beables are the information available at each event from its causal past, such as its causal predecessors and the energy and momentum they transfer to the event. We call this the view of an event. That is, we describe a causal universe that is composed of a set of partial views of itself. We propose that conscious perceptions are aspects of some views. This addresses the problem of why consciousness always involves awareness of a bundled grouping of qualia that define a momentary self. This gives a restricted form of panpsychism defined by a physically based selection principle which selects which views have experiential aspects. We further propose that only those views which are novel, in the sense that they are not duplicates of the view of any event in the event's own causal past, are the physical correlates of conscious experience.
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Тези доповідей конференцій з теми "Quantum principal bundles"

1

Sharygin, G. I. "A new construction of characteristic classes for noncommutative algebraic principal bundles." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-15.

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2

Fioresi, Rita, Emanuele Latini, Paolo Aschieri, and Thomas Weber. "Quantum Principal bundle and Non Commutative differential calculus." In Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity". Trieste, Italy: Sissa Medialab, 2022. http://dx.doi.org/10.22323/1.406.0280.

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