Kontsevich’s Deformation Quantization and Quantum Field Theory

Nima Moshayedi

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English

Springer International Publishing AG
13 August 2022

Calculus & mathematical analysis; Differential & Riemannian geometry; Topology; Quantum physics (quantum mechanics & quantum field theory)

Series: Lecture Notes in Mathematics

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.

By: Nima Moshayedi
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2022
Volume: 2311
Dimensions: Height: 235mm, Width: 155mm,
Weight: 539g
ISBN: 9783031051210
ISBN 10: 3031051211
Series: Lecture Notes in Mathematics
Pages: 336
Publication Date: 13 August 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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