Landsman, N. P. (Nicholas P.) creator text bibliography nyu New York Springer c1998 1998 monographic eng

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xix, 529 p. ; 24 cm. ill. ; This monograph draws on two traditions: the algebraic formulation of quantum mechanics and quantum field theory, and the geometric theory of classical mechanics. These are combined into a unified treatment of the theory of Poisson algebras and operator algebras, based on the duality between algebras of observables and pure state spaces with a transition probability. The theory of quantization and the classical limit is discussed from this perspective. This book should be accessible to mathematicians with some prior knowledge of classical and quantum mechanics, to mathematical physicists, and to theoretical physicists who have some background in functional analysis. I. Observables and Pure States -- II. Quantization and the Classical Limit -- III. Groups, Bundles, and Groupoids -- IV. Reduction and Induction. N.P. Landsman. Includes bibliographical references (p. [483]-520) and index. Quantum theory Mathematics Quantum field theory Mathematics Hilbert space Geometry, Differential Mathematical physics QC174.17.M35 L36 1998 530.12 LAM 038798318X (hardcover : alk. paper) 98018391 DLC 980407 20140915151955.0 2144263