Indistinguishable Classical ParticlesSpringer Science & Business Media, 30 lis 2008 - 160 In this book the concept of indistinguishability is defined for identical particles by the symmetry of the state. It applies, therefore, to both the classical and the quantum framework. The author describes symmetric statistical operators and classifies these by means of extreme points. 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 are 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. |
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9783540496243_5_OnlinePDF | 131 |
9783540496243_BookBackmatter_OnlinePDF | 144 |
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Assume binomial distribution Brillouin statistics cells characteristic function coherent concept of indistinguishability configuration random variables defined Definition denotes Dirac measure Dirichlet distribution distributed according exists exp(it extendible extreme points FD statistics FD symmetric Finetti measure Finetti's theorem follows G₁ Gn,i group occupation numbers Hilbert space holds hypergeometric distribution identical particles implies independent indistinguishable classical particles indistinguishable particles inequality integral representation interchangeable array interchangeable random variables Lemma macroscopic limit marginal MB statistics MB symmetric mixtures of Poisson multinomial distribution negative binomial distribution number of particles number random variables obtain occupation number random P(G₁ parastatistics Poisson distribution Poisson limit probability distribution probability measure Proof properties QED Remark quantum theory random vari random variables X1 Section sequence of interchangeable signed measure simplex Ssym(H subspace symmetric probability measure symmetric statistical operator unextendible variance vector