Esposito C. Formality Theory From Poisson Structures to Deformation Quantization

Springer International Publishing, 2015 — 90p. — (SpringerBriefs in Mathematical Physics 2) — ISBN: 978-3-319-09290-4 (eBook), 978-3-319-09289-8 (Softcover).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.Classical Mechanics and Poisson Structures
Deformation Quantization and Formality Theory
Kontsevich’s Formula and Globalization