03183oam 2200601 450 991025739520332120210715231426.03-540-49624-610.1007/978-3-540-49624-3(CKB)1000000000778087(SSID)ssj0000323936(PQKBManifestationID)12065020(PQKBTitleCode)TC0000323936(PQKBWorkID)10304476(PQKB)11043100(DE-He213)978-3-540-49624-3(MiAaPQ)EBC3088519(MiAaPQ)EBC6486095(PPN)155208233(EXLCZ)99100000000077808720210715d1997 uy 0engurnn|008mamaatxtccrIndistinguishable classical particles /Alexander Bach1st ed. 1997.Berlin, Heidelberg :Springer,[1997]©19971 online resource (VIII, 160 p.) Lecture Notes in Physics Monographs,0940-7677 ;44Bibliographic Level Mode of Issuance: Monograph3-540-62027-3 Includes bibliographical references.Indistinguishable Quantum Particles -- Indistinguishable Classical Particles -- De Finetti’s Theorem -- Historical and Conceptual Remarks.In this book the concept of indistinguishability is defined for identical particles by the symmetry of the state rather than by the symmetry of observables. It applies, therefore, to both the classical and the quantum framework. In this setting the particles of classical Maxwell-Boltzmann statistics are indistinguishable and independent. The author describes symmetric statistical operators and classifies these by means of extreme points and by means of extendibility properties. The three classical statistics are derived in abelian subalgebras. The classical theory of indistinguishability is based on the concept of interchangeable random variables which are classified by their extendibility properties. For the description of infinitely extendible interchangeable random variables de Finetti's theorem is derived and generalizations covering the Poisson limit and the central limit are presented. A characterization and interpretation of the integral representations of classical photon states in quantum optics is derived in abelian subalgebras. Unextendible indistinguishable particles are analyzed in the context of nonclassical photon states. The book addresses mathematical physicists and philosophers of science.Lecture Notes in Physics Monographs,0940-7677 ;44Maxwell-Boltzmann distribution lawCommutative algebraSymmetric operatorsMaxwell-Boltzmann distribution law.Commutative algebra.Symmetric operators.530.132Bach Alexander1946-60928MiAaPQMiAaPQUtOrBLWBOOK9910257395203321Indistinguishable Classical Particles376173UNINA