Geometric and Algebraic Topological Methods in Quantum Mechanics by Luigi Mangiarotti (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review the notions, concepts, etc, are introduced in a self-contained but condensed manner — Mathematical Reviews “Mathematical Reviews”

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book is great (not excellent) review of the subject in the title. I was hoping for more of an introductory approach and more math but was instead greeted by a lot of quantization and physics. I bought the book because I am looking at using quantum (the mathematical group not as in quantum physics) fibre bundle in my theory but there is very little about it in there. I have not found any other book that even has what I am looking for in quantum fibre bundles and this book remains the only option.

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