Relevant bibliographies by topics / Connes' noncommutative geometry

Academic literature on the topic 'Connes' noncommutative geometry'

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Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Connes' noncommutative geometry"

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Viet, Nguyen Ai. "A New Solution to the Structure Equation in Noncommutative Spacetime." Communications in Physics 24, no. 1 (March 12, 2014): 21. http://dx.doi.org/10.15625/0868-3166/24/1/3606.

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In this paper, starting from the common foundation of Connes' noncommutative geometry ( NCG)\cite{Connes1, Connes2, CoLo, Connes3}, various possible alternatives in the formulation of atheory of gravity in noncommutative spacetime are discussed indetails. The diversity in the final physical content of the theory is shown to be the consequence of the arbitrary choices in each construction steps. As an alternative in the last step, when the structure equations are to be solved, a minimal set of constraints on the torsion and connection is found to determine all the geometric notions in terms of the metric. In the Connes-Lott model of noncommutative spacetime, in order to keep the full spectrum of the discretized Kaluza-Klein theory \cite{VW2}, it is necessary to include the torsion in the generalized Einstein-Hilbert-Cartan action.
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AASTRUP, JOHANNES, and JESPER MØLLER GRIMSTRUP. "INTERSECTING CONNES NONCOMMUTATIVE GEOMETRY WITH QUANTUM GRAVITY." International Journal of Modern Physics A 22, no. 08n09 (April 10, 2007): 1589–603. http://dx.doi.org/10.1142/s0217751x07035306.

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An intersection of noncommutative geometry and loop quantum gravity is proposed. Alain Connes' noncommutative geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is known. In this paper we consider the noncommutative algebra of holonomy loops on a functional space of certain spin-connections. The construction of a spectral triple is outlined and ideas on interpretation and classical limit are presented.
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SCHÜCKER, THOMAS. "NONCOMMUTATIVE GEOMETRY AND THE STANDARD MODEL." International Journal of Modern Physics A 20, no. 11 (April 30, 2005): 2471–80. http://dx.doi.org/10.1142/s0217751x05024791.

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LIZZI, F., G. MANGANO, G. MIELE, and G. SPARANO. "MIRROR FERMIONS IN NONCOMMUTATIVE GEOMETRY." Modern Physics Letters A 13, no. 03 (January 30, 1998): 231–37. http://dx.doi.org/10.1142/s0217732398000292.

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In a recent paper we pointed out the presence of extra fermionic degrees of freedom in a chiral gauge theory based on Connes' noncommutative geometry. Here we propose a mechanism which provides a high mass to these mirror states, so that they decouple from low energy physics.
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Sergeev, A. G. "Spin geometry of Dirac and noncommutative geometry of Connes." Proceedings of the Steklov Institute of Mathematics 298, no. 1 (August 2017): 256–93. http://dx.doi.org/10.1134/s0081543817060177.

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Landi, Giovanni. "BOOK REVIEW: Noncommutative Geometry, by Alain Connes." General Relativity and Gravitation 30, no. 10 (October 1998): 1543–48. http://dx.doi.org/10.1023/a:1018821310333.

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VAN DEN DUNGEN, KOEN, and WALTER D. VAN SUIJLEKOM. "PARTICLE PHYSICS FROM ALMOST-COMMUTATIVE SPACETIMES." Reviews in Mathematical Physics 24, no. 09 (October 2012): 1230004. http://dx.doi.org/10.1142/s0129055x1230004x.

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Our aim in this review paper is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this paper we introduce the ideas and concepts from noncommutative geometry using physicists' terminology, gearing towards the predictions that can be derived from the noncommutative description. Focusing on a light package of noncommutative geometry (so-called "almost-commutative manifolds"), we shall introduce in steps: electrodynamics, the electroweak model, culminating in the full Standard Model. We hope that our approach helps in understanding the role noncommutative geometry could play in describing particle physics models, eventually unifying them with Einstein's (geometrical) theory of gravity.
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LIZZI, F., G. MANGANO, G. MIELE, and G. SPARANO. "CONSTRAINTS ON UNIFIED GAUGE THEORIES FROM NONCOMMUTATIVE GEOMETRY." Modern Physics Letters A 11, no. 32n33 (October 30, 1996): 2561–72. http://dx.doi.org/10.1142/s0217732396002575.

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We analyze the possibility to extend the Connes and Lott reformulation of the standard model to larger unified gauge groups. Noncommutative geometry imposes very stringent constraints on the possible theories, and remarkably, the analysis seems to suggest that no larger gauge groups are compatible with the noncommutative structure, unless one enlarges the fermionic degrees of freedom, namely the number of particles.
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RENNIE, A. "COMMUTATIVE GEOMETRIES ARE SPIN MANIFOLDS." Reviews in Mathematical Physics 13, no. 04 (April 2001): 409–64. http://dx.doi.org/10.1142/s0129055x01000673.

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In [1], Connes presented axioms governing noncommutative geometry. He went on to claim that when specialised to the commutative case, these axioms recover spin or spinc geometry depending on whether the geometry is "real" or not. We attempt to flesh out the details of Connes' ideas. As an illustration we present a proof of his claim, partly extending the validity of the result to pseudo-Riemannian spin manifolds. Throughout we are as explicit and elementary as possible.
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Várilly, Joseph C., and JoséM Gracia-Bondía. "Connes' noncommutative differential geometry and the standard model." Journal of Geometry and Physics 12, no. 4 (November 1993): 223–301. http://dx.doi.org/10.1016/0393-0440(93)90038-g.

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Dissertations / Theses on the topic "Connes' noncommutative geometry"

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Dias, David Pires. "O caráter de Chern-Connes para C*-sistemas dinâmicos calculado em algumas álgebras de operadores pseudodiferenciais." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05082008-164858/.

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Dado um C$^*$-sistema dinâmico $(A, G, \\alpha)$ define-se um homomorfismo, denominado de caráter de Chern-Connes, que leva elementos de $K_0(A) \\oplus K_1(A)$, grupos de K-teoria da C$^*$-álgebra $A$, em $H_{\\mathbb}^*(G)$, anel da cohomologia real de deRham do grupo de Lie $G$. Utilizando essa definição, nós calculamos explicitamente esse homomorfismo para os exemplos $(\\overline{\\Psi_^0(S^1)}, S^1, \\alpha)$ e $(\\overline{\\Psi_^0(S^2)}, SO(3), \\alpha)$, onde $\\overline{\\Psi_^0(M)}$ denota a C$^*$-álgebra gerada pelos operadores pseudodiferenciais clássicos de ordem zero da variedade $M$ e $\\alpha$ a ação de conjugação pela representação regular (translações).
Given a C$^*$-dynamical system $(A, G, \\alpha)$ one defines a homomorphism, called the Chern-Connes character, that take an element in $K_0(A) \\oplus K_1(A)$, the K-theory groups of the C$^*$-algebra $A$, and maps it into $H_{\\mathbb}^*(G)$, the real deRham cohomology ring of $G$. We explictly compute this homomorphism for the examples $(\\overline{\\Psi_^0(S^1)}, S^1, \\alpha)$ and $(\\overline{\\Psi_^0(S^2)}, SO(3), \\alpha)$, where $\\overline{\\Psi_^0(M)}$ denotes the C$^*$-álgebra gene\\-rated by the classical pseudodifferential operators of zero order in the manifold $M$ and $\\alpha$ the action of conjugation by the regular representation (translations).
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Van, Den Dungen Koen. "Lorentzian geometry and physics in Kasparov's theory." Phd thesis, 2015. http://hdl.handle.net/1885/15240.

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We study two geometric themes, Lorentzian geometry and gauge theory, from the perspective of Connes’ noncommutative geometry and (the unbounded version of) Kasparov’s KK-theory. Lorentzian geometry is the mathematical framework underlying Einstein’s description of gravity. The geometric formulation of a gauge theory (in terms of principal bundles) offers a classical description for the interactions between particles. The underlying motivation is the hope that this noncommutative approach may lead to a unified description of gauge theories coupled with gravity on a Lorentzian manifold. The main objects in noncommutative geometry are spectral triples, which encompass and generalise Riemannian spin manifolds. A spectral triple defines a class in K-homology, via which one can access the topology of the (noncommutative) manifold. In this thesis we present two possible definitions for ‘Lorentian spectral triples’, which offer noncommutative generalisations of Lorentzian manifolds as well. We will prove that both definitions preserve the link with analytic K-homology. We will describe under which conditions Lorentzian (or pseudo- Riemannian) manifolds satisfy these definitions. Another main example is the harmonic oscillator, which in particular shows that our framework allows to deal with more than just metrics of indefinite signature. In the context of noncommutative geometry, the description of a gauge theory can be obtained from so-called almost-commutative manifolds. While the usual approach yields by default a topologically trivial gauge theory (in the sense that the corresponding principal fibre bundle is globally trivial), we show in this thesis that the framework can be adapted, using the internal unbounded Kasparov product, to allow for globally non-trivial gauge theories as well. Finally, we combine the two themes of Lorentzian geometry and gauge theory, and we define Krein spectral triples, which generalise spectral triples from Hilbert spaces to Krein spaces. We use this definition to construct almost-commutative Lorentzian manifolds. Furthermore, we propose a Lorentzian alternative for the fermionic action, which allows to derive (the fermionic part of) the Lagrangian of a gauge theory. We show that our alternative action recovers exactly the correct physical Lagrangian.
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Books on the topic "Connes' noncommutative geometry"

1

Introduction to the Baum-Connes conjecture. Basel: Birkhäuser Verlag, 2002.

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2

Kastler, Daniel. Cyclic cohomology within the differential envelope: An introduction to Alain Connes' non-commutative differential geometry. Paris: Hermann, 1988.

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Connes, Alain. Quanta of maths: Conference in honor of Alain Connes, non commutative geometry, Institut Henri Poincaré, Institut des hautes études scientifiques, Institut de mathématiques de Jussieu, Paris, France, March 29-April 6, 2007. Providence, R.I: American Mathematical Society, 2010.

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Poincaré, Institut Henri, Institut des hautes études scientifiques (Paris, France), and Institut de mathématiques de Jussieu, eds. Quanta of maths: Conference in honor of Alain Connes, non commutative geometry, Institut Henri Poincaré, Institut des hautes études scientifiques, Institut de mathématiques de Jussieu, Paris, France, March 29-April 6, 2007. Providence, R.I: American Mathematical Society, 2010.

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Argentina) Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry (3rd 2010 Buenos Aires. Topics in noncommutative geometry: Third Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry, Universidad de Buenos Aires, Buenos Aires, Argentina, July 26-August 6, 2010. Edited by Cortiñas, Guillermo, editor of compilation. Providence, RI: American Mathematical Society, 2012.

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Noncommutative geometry and global analysis: Conference in honor of Henri Moscovici, June 29-July 4, 2009, Bonn, Germany. Providence, R.I: American Mathematical Society, 2011.

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Valette, Alain. Introduction to the Baum-Connes Conjecture. Birkhauser Verlag, 2012.

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Khalkhali, Masoud, Nigel Higson, Caterina Consani, Ali Chamseddine, and Henri Moscovici. Advances in Noncommutative Geometry: On the Occasion of Alain Connes' 70th Birthday. Springer International Publishing AG, 2021.

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Khalkhali, Masoud, Nigel Higson, Caterina Consani, Guoliang Yu, Ali Chamseddine, and Henri Moscovici. Advances in Noncommutative Geometry: On the Occasion of Alain Connes' 70th Birthday. Springer, 2020.

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Book chapters on the topic "Connes' noncommutative geometry"

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Gracia-Bondía, José M., Joseph C. Várilly, and Héctor Figueroa. "Connes’ Spin Manifold Theorem." In Elements of Noncommutative Geometry, 487–515. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0005-5_11.

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Gracia-Bondía, José M., Joseph C. Várilly, and Héctor Figueroa. "Kreimer-Connes-Moscovici Algebras." In Elements of Noncommutative Geometry, 597–640. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0005-5_14.

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Aparicio, Maria Paula Gomez, Pierre Julg, and Alain Valette. "The Baum–Connes conjecture: an extended survey." In Advances in Noncommutative Geometry, 127–244. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29597-4_3.

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Nest, Ryszard, Elmar Vogt, and Wend Werner. "Spectral Action and the Connes-Chamsedinne Model." In Noncommutative Geometry and the Standard Model of Elementary Particle Physics, 109–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-46082-9_6.

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Alberti, Peter M., and Reiner Matthes. "Connes’ Trace Formula and Dirac Realization of Maxwell and Yang-Mills Action." In Noncommutative Geometry and the Standard Model of Elementary Particle Physics, 40–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-46082-9_4.

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Skandalis, Georges. "Noncommutative Geometry, the Transverse Signature Operator, and Hopf Algebras [after A. Connes and H. Moscovici]." In Encyclopaedia of Mathematical Sciences, 115–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06444-3_3.

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"9. Connes geometries." In Noncommutative Geometry, 207–16. De Gruyter, 2017. http://dx.doi.org/10.1515/9783110545258-011.

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"11 Connes geometries." In Noncommutative Geometry, 313–24. De Gruyter, 2022. http://dx.doi.org/10.1515/9783110788709-011.

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KOSTRO, LUDWIK. "Einstein’s Ultrareferential Spacetime and Alain Connes’ Noncommutative Geometry." In Fundamental Physics at the Vigier Centenary, 265–79. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811246463_0008.

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