Formality Theory [electronic resource] : From Poisson Structures to Deformation Quantization /
Esposito, Chiara.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
Introduction -- Classical mechanics and Poisson structures -- Deformation quantization and formality theory -- Kontsevich’s Formula and Globalization -- Appendix -- Vector bundles -- Cohomology -- Index.
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.
Quantum field theory.
String theory.
Mathematical physics.
Functional analysis.
Quantum Field Theories, String Theory.
Mathematical Physics.
Functional Analysis.