Lectures On Deformation Quantisation: From Moyal Product To Kontsevich's Formality Theorem
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A01=Georgy Igorevich Sharygin
Author_Georgy Igorevich Sharygin
Category=PHQ
Category=PHU
Deformation Quantisation
Deformation Quantization
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Fedosov Quantisation
Fedosov Quantization
Kontsevich's Formality Theorem
Quantum Theory
Product details
- ISBN 9789811297809
- Publication Date: 27 Jun 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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Principles of classical Hamiltonian mechanics say that the evolution of a dynamical system is determined by the Poisson bracket of observable functions with the given Hamiltonian function of the system. In Quantum Mechanics, these principles are modified so that the algebra of observable functions should be replaced by a noncommutative algebra of operators and the Poisson bracket by their commutator so that the canonical commutation relations hold. Thus, working with quantum systems, we must determine the "quantisation" of our observables, i.e. to choose a noncommutative algebra whose elements would play the role of the observables. With some modifications, this question is the main content of the Deformation Quantisation problem formulated in 1978 by Flato and others.This book is based on the course that the author taught in the Fall semester of 2019 at Peking University. The main purpose of that course and of this book is to acquaint the reader with the vast scope of ideas related to the Deformation Quantisation of Poisson manifolds. The book begins with Quantum Mechanics and Moyal product formula and covers the three main constructions that solve the Deformation Quantisation problem: Lecomte and de Wilde deformation of symplectic manifolds, Fedosov's Quantisation theory and Kontsevich's formality theorem. In the appendices, the Tamarkin's proof of formality theorem is outlined.The book is written in a reader-friendly manner and is as self-contained as possible. It includes several sets of problems and exercises that will help the reader to master the material.
