Quantization, Geometry and Noncommutative Structures in Mathematics and Physics
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Quantization, Geometry and Noncommutative Structures in Mathematics and Physics
Cardona, Alexander; Paycha, Sylvie; Ocampo, Hernan; Morales, Pedro; Reyes Lega, Andres F.
Springer International Publishing AG
05/2018
341
Mole
Inglês
9783319880266
15 a 20 dias
5329
Descrição não disponível.
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics (A. Cardona, H. Ocampo, P. Morales, S. Paycha, A.F. Reyes Lega (Eds.)).- General Overview (Alexander Cardona, Sylvie Paycha and Andres F. Reyes Lega).- Introduction.- Poisson Geometry and Classical Dynamics.- Geometric and Deformation Quantization.- Noncommutative Geometry and Quantum Groups.- Deformation Quantization and Group Actions (Simone Gutt).- What do we mean by quantization?.- Deformation Quantization.- Fedosov's star products on a symplectic manifold.- Classification of Poisson deformations and star products.- Star products on Poisson manifolds and formality.- Group actions in deformation quantization.- Reduction in deformation quantization.- Some remarks about convergence.- . Principal fiber bundles in non-commutative geometry (Christian Kassel).- Introduction.- Review of principal fiber bundles.- Basic ideas of non-commutative geometry.- From groups to Hopf algebras.- Quantum groups associated with SL2(C).- Group actions in non-commutative geometry.- Hopf Galois extensions.- Flat deformations of Hopf algebras.- An Introduction to Nichols Algebras (Nicolas Andruskiewitsch).- Preliminaries.- Braided tensor categories.- Nichols algebras.- Classes of Nichols algebras.- Quantum Field Theory in Curved Space-Time (Andres F. Reyes Lega).- Introduction.- Quantum Field Theory in Minkowski Space-Time.- Quantum Field Theory in Curved Space-Time.- Cosmology.- An Introduction to Pure Spinor Superstring Theory (Nathan Berkovits and Humberto Gomez).- Introduction.- Particle and Superparticle.- Pure Spinor Superstring.- Appendix.- Introduction to Elliptic Fibrations (Mboyo Esole).- Introduction.- Elliptic curves over C.- Elliptic fibrations.- Kodaira-Neron classification of singular fibers.- Miranda models.- Batalin-Vilkovisky formalism as a theory of integration for polyvectors (Pierre J. Clavier and Viet Dang Nguyen).- Motivations and program.- BV integral.- Gauge fixing.- Master equations.- Conclusion.- Split Chern-Simons theory in the BV-BFV formalism (Alberto S. Cattaneo, Pavel Mnev, and Konstantin Wernli).- Introduction.- Overview of the BV and BV-BFV formalisms.- Chern-Simons theory as a BF-like theory.- Split Chern-Simons theory on the solid torus.- Conclusions and outlook.- Weighted direct product of spectral triples (Kevin Falk).- Introduction and motivation. -Weighted direct product of spectral triples.- Example of weighted direct product with Toeplitz operators.- Index.
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deformation quantization;noncommutative geometry;Poisson manifold;principal fibre boundles;group actions;Elloptic fibrations;Poisson geometry;Quantum groups;Fedosov's star products;Hopf algebras;Hopf Galois extensions;Spectral triples;Toeplitz operators;Nichols algebras;Pure spinor superstrings;Kodaira-Neron classification;Miranda models;Batalin-Vilkovisky formalism;polyvectors;Chern-Simons theory
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics (A. Cardona, H. Ocampo, P. Morales, S. Paycha, A.F. Reyes Lega (Eds.)).- General Overview (Alexander Cardona, Sylvie Paycha and Andres F. Reyes Lega).- Introduction.- Poisson Geometry and Classical Dynamics.- Geometric and Deformation Quantization.- Noncommutative Geometry and Quantum Groups.- Deformation Quantization and Group Actions (Simone Gutt).- What do we mean by quantization?.- Deformation Quantization.- Fedosov's star products on a symplectic manifold.- Classification of Poisson deformations and star products.- Star products on Poisson manifolds and formality.- Group actions in deformation quantization.- Reduction in deformation quantization.- Some remarks about convergence.- . Principal fiber bundles in non-commutative geometry (Christian Kassel).- Introduction.- Review of principal fiber bundles.- Basic ideas of non-commutative geometry.- From groups to Hopf algebras.- Quantum groups associated with SL2(C).- Group actions in non-commutative geometry.- Hopf Galois extensions.- Flat deformations of Hopf algebras.- An Introduction to Nichols Algebras (Nicolas Andruskiewitsch).- Preliminaries.- Braided tensor categories.- Nichols algebras.- Classes of Nichols algebras.- Quantum Field Theory in Curved Space-Time (Andres F. Reyes Lega).- Introduction.- Quantum Field Theory in Minkowski Space-Time.- Quantum Field Theory in Curved Space-Time.- Cosmology.- An Introduction to Pure Spinor Superstring Theory (Nathan Berkovits and Humberto Gomez).- Introduction.- Particle and Superparticle.- Pure Spinor Superstring.- Appendix.- Introduction to Elliptic Fibrations (Mboyo Esole).- Introduction.- Elliptic curves over C.- Elliptic fibrations.- Kodaira-Neron classification of singular fibers.- Miranda models.- Batalin-Vilkovisky formalism as a theory of integration for polyvectors (Pierre J. Clavier and Viet Dang Nguyen).- Motivations and program.- BV integral.- Gauge fixing.- Master equations.- Conclusion.- Split Chern-Simons theory in the BV-BFV formalism (Alberto S. Cattaneo, Pavel Mnev, and Konstantin Wernli).- Introduction.- Overview of the BV and BV-BFV formalisms.- Chern-Simons theory as a BF-like theory.- Split Chern-Simons theory on the solid torus.- Conclusions and outlook.- Weighted direct product of spectral triples (Kevin Falk).- Introduction and motivation. -Weighted direct product of spectral triples.- Example of weighted direct product with Toeplitz operators.- Index.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
deformation quantization;noncommutative geometry;Poisson manifold;principal fibre boundles;group actions;Elloptic fibrations;Poisson geometry;Quantum groups;Fedosov's star products;Hopf algebras;Hopf Galois extensions;Spectral triples;Toeplitz operators;Nichols algebras;Pure spinor superstrings;Kodaira-Neron classification;Miranda models;Batalin-Vilkovisky formalism;polyvectors;Chern-Simons theory
