01885fam a2200349 a 45000010008000000030008000080050017000160080041000330100017000740200040000910350020001310350023001510350017001740400036001910500027002270820020002541000035002742450082003092600034003912630009004253000035004343650016004695040066004855050157005515200460007085200222011686500033013906500039014236500019014626500028014816500026015092144263BD-DhUL20140915151955.0980407s1998    nyu      b    001 0 eng    a   98018391   a038798318X (hardcover : alk. paper)  a(OCoLC)38966087  a(OCoLC)ocm38966087  a(NNC)2144263  aDLCcDLCdNNCdOrLoB-BdBD-DhUL00aQC174.17.M35bL36 199800a530.12221bLAM1 aLandsman, N. P.q(Nicholas P.)10aMathematical topics between classical and quantum mechanics /cN.P. Landsman.  aNew York :bSpringer,cc1998.  a9809  axix, 529 p. ;c24 cm.bill. ;   aUSDb125.96  aIncludes bibliographical references (p. [483]-520) and index.00gI.tObservables and Pure States --gII.tQuantization and the Classical Limit --gIII.tGroups, Bundles, and Groupoids --gIV.tReduction and Induction.  aThis 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.8 aThis 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. 0aQuantum theoryxMathematics. 0aQuantum field theoryxMathematics. 0aHilbert space. 0aGeometry, Differential. 0aMathematical physics.