Formality Theory: From Poisson structures to Deformation Quantization by Chiara EspositoFormality Theory: From Poisson structures to Deformation Quantization by Chiara Esposito

Formality Theory: From Poisson structures to Deformation Quantization

byChiara Esposito

Paperback | September 18, 2014

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This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.

Title:Formality Theory: From Poisson structures to Deformation QuantizationFormat:PaperbackDimensions:90 pagesPublished:September 18, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319092898

ISBN - 13:9783319092898

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Table of Contents

Introduction.- Classical mechanics and Poisson structures.- Deformation quantization and formality theory.- Kontsevich's Formula and Globalization.- Appendix.- Vector bundles.- Cohomology.- Index.

Editorial Reviews

"The formality theorem gave deep insight into the homological algebra of smooth functions on a manifold. Many applications have grown out of this investigation, too many to mention here. . the author explains its implications together with its origins in the theory of quantization. This is a valuable contribution since the formulation of the statement requires some sophisticated preparation, which is carefully discussed in this booklet." (Stefan Waldmann, Mathematical Reviews, February, 2016)