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Kontsevich’s Deformation Quantization and Quantum Field Theory

  • Book
  • © 2022

Overview

Authors:
  1. Nima Moshayedi

    1. Department of Mathematics, University of California, Berkeley, USA

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  • 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

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2311)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Nima Moshayedi
    Pages 1-5

  3. Foundations of Differential Geometry

    • Nima Moshayedi
    Pages 7-84

  4. Symplectic Geometry

    • Nima Moshayedi
    Pages 85-139

  5. Poisson Geometry

    • Nima Moshayedi
    Pages 141-163

  6. Deformation Quantization

    • Nima Moshayedi
    Pages 165-232

  7. Quantum Field Theoretic Approach to Deformation Quantization

    • Nima Moshayedi
    Pages 233-320

  8. Back Matter

    Pages 321-336
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of California, Berkeley, USA

    Nima Moshayedi

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