Kontsevich¿s Deformation Quantization and ...

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Beschreibung

This book provides an introduction to deformation quantization and its relation to quantum field theory, with a focus on the constructions of Kontsevich and Cattaneo & Felder. This subject originated from an attempt to understand the mathematical structure when passing from a commutative classical algebra of observables to a non-commutative quantum algebra of observables. Developing deformation quantization as a semi-classical limit of the expectation value for a certain observable with respect to a special sigma model, the book carefully describes the relationship between the involved algebraic and field-theoretic methods. The connection to quantum field theory leads to the study of important new field theories and to insights in other parts of mathematics such as symplectic and Poisson geometry, and integrable systems.

Based on lectures given by the author at the University of Zurich, the book will be of interest to graduate students in mathematics or theoretical physics. Readers will be able to begin the first chapter after a basic course in Analysis, Linear Algebra and Topology, and references are provided for more advanced prerequisites.

Zusammenfassung

Explains the connection between Kontsevich's deformation quantization and QFT

Provides a concise introduction to Differential, Symplectic and Poisson Geometry

Includes numerous examples and exercises

Inhaltsverzeichnis

- 1. Introduction. - 2. Foundations of Differential Geometry. - 3. Symplectic Geometry. - 4. Poisson Geometry. - 5. Deformation Quantization. - 6. Quantum Field Theoretic Approach to Deformation Quantization.

Details

Erscheinungsjahr:	2022
Fachbereich:	Geometrie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Lecture Notes in Mathematics
Inhalt:	xiii 336 S. 40 s/w Illustr. 1 farbige Illustr. 336 p. 41 illus. 1 illus. in color.
ISBN-13:	9783031051210
ISBN-10:	3031051211
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Moshayedi, Nima
Auflage:	1st ed. 2022
Hersteller:	Springer International Publishing Springer International Publishing AG Lecture Notes in Mathematics
Maße:	235 x 155 x 20 mm
Von/Mit:	Nima Moshayedi
Erscheinungsdatum:	13.08.2022
Gewicht:	0,534 kg