Quantization, Geometry and Noncommutative Structures in Mathematics and Physics

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Cardona, Alexander (Επιμελητής έκδοσης), Morales, Pedro (Επιμελητής έκδοσης), Ocampo, Hernán (Επιμελητής έκδοσης), Paycha, Sylvie (Επιμελητής έκδοσης), Reyes Lega, Andrés F. (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Σειρά: Mathematical Physics Studies,
• Θέματα: Physics.; Algebraic geometry.; Mathematical physics.; Quantum field theory.; String theory.; Quantum Field Theories, String Theory.; Mathematical Physics.; Algebraic Geometry.

This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of qu...

Πίνακας περιεχομένων:

• 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 Andrés 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 (Nicolás Andruskiewitsch)
• Preliminaries
• Braided tensor categories
• Nichols algebras
• Classes of Nichols algebras
• Quantum Field Theory in Curved Space-Time (Andrés 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-Néron 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.