Kontsevich’s Deformation Quantization and Quantum Field Theory

Nima Moshayedi (Autor)

Buch | Softcover

XIII, 336 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-05121-0 (ISBN)

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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.

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

Erscheinungsdatum	14.08.2022
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIII, 336 p. 41 illus., 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	536 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	AKSZ Theories • Batalin-Vilkovisky • BRST • Cattaneo-Felder • configuration spaces • Deformation quantization • Differential Geometry • Faddeev-Popov • Fedosov Quantization • Feynman graphs • Gauge Theory • Kontsevich • L-infinity Algebras • Path Integral Quantization • poisson geometry • Poisson Sigma Model • quantum field theory • Symplectic Geometry • Toplogical Quantum Field Theory • Weyl-Moyal Quantization
ISBN-10	3-031-05121-1 / 3031051211
ISBN-13	978-3-031-05121-0 / 9783031051210
Zustand	Neuware