01964fam a2200385 a 4500 2144263 BD-DhUL 20140915151955.0 980407s1998 nyu b 001 0 eng 98018391 038798318X (hardcover : alk. paper) (OCoLC)38966087 (OCoLC)ocm38966087 (NNC)2144263 DLC DLC NNC OrLoB-B BD-DhUL QC174.17.M35 L36 1998 530.12 21 LAM Landsman, N. P. (Nicholas P.) Mathematical topics between classical and quantum mechanics / N.P. Landsman. New York : Springer, c1998. 9809 xix, 529 p. ; 24 cm. ill. ; USD 125.96 Includes bibliographical references (p. [483]-520) and index. I. Observables and Pure States -- II. Quantization and the Classical Limit -- III. Groups, Bundles, and Groupoids -- IV. Reduction and Induction. 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. Quantum theory Mathematics. Quantum field theory Mathematics. Hilbert space. Geometry, Differential. Mathematical physics. AUTH TOC ddc BK 10618 10618 0 0 ddc 0 530_120000000000000_LAM 0 NFIC 18918 DUSL DUSL GEN 2010-12-19 purcheses 530.12 LAM 454849 2014-09-15 2014-09-15 BK