Kontsevich’s Deformation Quantization and Quantum Field Theory
Seiten
2022
|
1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-05121-0 (ISBN)
Springer International Publishing (Verlag)
978-3-031-05121-0 (ISBN)
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 |
| 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 |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Band 5: Hydraulik, Stromfadentheorie, Wellentheorie, Gasdynamik
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 83,90
