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Graduate Studies in Mathematics
2008; 387 pp; hardcover
List Price: US$75
Member Price: US$60
Order Code: GSM/95
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.
Graduate students and research mathematicians interested in mathematical aspects of quantum mechanics.
"...heaven-sent to the aforementioned analytic number theorist, i.e., me, because it is mathematics, not physics: the exposition is peppered with definitions and theorems, and proofs!, proofs!, proofs!..."
-- Michael Berg for MAA Reviews
"By a clever selection of the material and the clear way of exposing it, the book is recommended for graduate students in mathematics looking for applications in physics, as well as for student in physics desiring to be acquainted, in a rigorous but, at the same time, quick and accessible manner, with the basic mathematical tools used in quantum mathematics."
-- Studia Universitatis Babes-Bolyai, Mathematica
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