Quantum Mechanics for Mathematicians (Graduate Studies in Mathematics) (Graduate Studies in Mathematics Volume 95)

Main subject categories: • Primary 81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory • Mathematical physics • Mathematical foundations of quantum mechanics • Classical mechanicsThis book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. In addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrödinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature.This book is written in a concise style with careful attention to precise mathematics formulation of methods and results. Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory.Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis. This Book Provides A Comprehensive Treatment Of Quantum Mechanics From A Mathematics Perspective And Is Accessible To Mathematicians Starting With Second-year Graduate Students. In Addition To Traditional Topics, Like Classical Mechanics, Mathematical Foundations Of Quantum Mechanics, Quantization, And The Schrodinger Equation, This Book Gives A Mathematical Treatment Of Systems Of Identical Particles With Spin, And It Introduces The Reader To Functional Methods In Quantum Mechanics. This Includes The Feynman Path Integral Approach To Quantum Mechanics, Integration In Functional Spaces, The Relation Between Feynman And Wiener Integrals, Gaussian Integration And Regularized Determinants Of Differential Operators, Fermion Systems And Integration Over Anticommuting (grassmann) Variables, Supersymmetry And Localization In Loop Spaces, And Supersymmetric Derivation Of The Atiyah-singer Formula For The Index Of The Dirac Operator. This Book Is Written In A Concise Style With Careful Attention To Precise Mathematics Formulation Of Methods And Results. Numerous Problems, From Routine To Advanced, Help The Reader To Master The Subject. In Addition To Providing A Fundamental Knowledge Of Quantum Mechanics, This Book Could Also Serve As A Bridge For Studying More Advanced Topics In Quantum Physics, Among Them Quantum Field Theory.--jacket. Classical Mechanics -- Basic Principles Of Quantum Mechanics -- Schrödinger Equation -- Spin And Identical Particles -- Functional Methods And Supersymmetry -- Path Integral Formulation Of Quantum Mechanics -- Integration In Functional Spaces -- Fermion Systems -- Supersymmetry. Leon A. Takhtajan. Includes Bibliographical References (p. 373-381) And Index. This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. In addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results. Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis. This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. In addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrödinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results. Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis. "This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. In addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator." "This book is written in a concise style with careful attention to precise mathematics formulation of methods and results. Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory."--Résumé de l'éditeur Takhtadzhian, also spelled Takhtajan, (mathematics, Stony Brook U.) offers a textbook based on a course he has long taught to second year graduates of mathematics who were assumed to have no prior knowledge of physics. He introduces the basic concepts and methods of quantum mechanics, emphasizing those aspects that have influenced the recent course of mathematics in the same manner that classical physics did from the 17th to the 19th centuries. The material can be used for a one-year course or two one-semester courses. Annotation 2008 Book News, Inc., Portland, OR (booknews.com)