Kontsevich's Deformation Quantization and Quantum Field Theory
暫譯: 康茨維奇的變形量子化與量子場論

Moshayedi, Nima

  • 出版商: Springer
  • 出版日期: 2022-08-13
  • 售價: $2,990
  • 貴賓價: 9.5$2,841
  • 語言: 英文
  • 頁數: 270
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031051211
  • ISBN-13: 9783031051210
  • 相關分類: 量子 Quantum
  • 海外代購書籍(需單獨結帳)

商品描述

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.

 

商品描述(中文翻譯)

本書介紹了變形量子化及其與量子場論的關係,重點在於Kontsevich以及Cattaneo & Felder的構造。這一主題源於試圖理解從可交換的經典可觀測量代數轉變為非可交換的量子可觀測量代數時的數學結構。發展變形量子化作為某個可觀測量相對於特定σ模型的期望值的半經典極限,本書仔細描述了所涉及的代數方法和場論方法之間的關係。與量子場論的聯繫引導我們研究重要的新場論,並對數學的其他部分如辛幾何、泊松幾何和可積系統提供了見解。本書基於作者在蘇黎世大學的講座,將對數學或理論物理的研究生感興趣。讀者在完成基本的分析、線性代數和拓撲課程後即可開始閱讀第一章,並提供了更高級的先修參考資料。