Geometric and Algebraic Topological Methods in Quantum Mechanics

Geometric and Algebraic Topological Methods in Quantum Mechanics
ISBN-10
9814481149
ISBN-13
9789814481144
Category
Science
Pages
720
Language
English
Published
2005-01-27
Publisher
World Scientific
Authors
Giovanni Giachetta, Luigi Mangiarotti, Gennadi A Sardanashvily

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. Contents:Commutative GeometryClassical Hamiltonian SystemsAlgebraic QuantizationGeometry of Algebraic QuantizationGeometric QuantizationSupergeometryDeformation QuantizationNon-Commutative GeometryGeometry of Quantum Groups Readership: Theoreticians and mathematicians of postgraduate and research level. Keywords:Algebraic Quantum Theory;Poisson Manifold;Hilbert Manifold;Geometric Quantization;Deformation Quantization;Supergeometry;Noncommutative Geometry;Constraint System;Quantum GroupKey Features:The book collects all the advanced methods of quantization in the last decadeIt presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.Reviews:“This book is well-written and I am convinced that it will be useful to all those interested in quantum theory.”Zentralblatt MATH “With respect to a propsective reader having a reasonably good background in mathematics, the notions, concepts, etc, are introduced in a self-contained but condensed manner … The book gives a very helpful supply of mathematical tools needed by a theoretical or mathematical physicist to effect entry into some of the new directions in theoretical physics. Also, a mathematician might appreciate the condensed presentation of definitions and results in one of the modern fields of mathematics for which one may be seeking an overview.”Mathematical Reviews '

Get the book

Amazon.com
Amazon.com
Search the book
eBay.com
eBay.com
Search the book

Other editions

Similar books