by Giovanni Giachetta (University of Camerino, Italy), Luigi Mangiarotti (University of Camerino, Italy), & Gennadi Sardanashvily (Moscow State University, Russia)

Table of Contents (81k)
Preface (34k)
Introduction (550k)

In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric 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 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.

• Commutative Geometry
• Classical Hamiltonian Systems
• Algebraic Quantization
• Geometry of Algebraic Quantization
• Geometric Quantization
• Supergeometry
• Deformation Quantization
• Non-Commutative Geometry
• Geometry of Quantum Groups