2004/10/16 by G. Giachetta, L. Mangiarotti, G. Sardanashvily
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP #quant-ph
published as World Scientific, Singapore, 2005 · Preface, Contents and Bibliography, 26 pages
arxiv created 2004/10/16 · arxiv updated 2009/12/01
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The present book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.