Kontsevich's deformation quantization and quantum field theory
Author(s)
Bibliographic Information
Kontsevich's deformation quantization and quantum field theory
（Lecture notes in mathematics, 2311）
Springer, c2022
1st ed
- : pbk
Available at / 30 libraries
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Yukawa Institute for Theoretical Physics, Kyoto University基物研
: pbkH||LEC||MA||2311200043710567
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkL/N||LNM||2311200043575577
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Note
Includes bibliographical references (p. 321-327) and index
Description and Table of Contents
Description
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.
Table of Contents
- 1. Introduction. - 2. Foundations of Differential Geometry. - 3. Symplectic Geometry. - 4. Poisson Geometry. - 5. Deformation Quantization. - 6. Quantum Field Theoretic Approach to Deformation Quantization.
by "Nielsen BookData"