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Kontsevich's deformation quantization and quantum field theory / Nima Moshayedi.

9783031051227 (electronic bk.)
303105122X (electronic bk.)
9783031051210
3031051211

Cham : Springer, [2022]

©2022

English

1 online resource (xiii, 336 pages) : illustrations (some color).

10.1007/978-3-031-05122-7 doi

QC174.52.D45

530.14/3

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.

Includes bibliographical references and index.

Access limited to authorized users.

Online resource; title from PDF title page (SpringerLink, viewed August 23, 2022).

Lecture notes in mathematics (Springer-Verlag) ; 2311. 1617-9692

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