Author(s): Randall Espinoza
Series: PhD Thesis
Publisher: University of Illinois at Chicago
Year: 2005
1 GENERALIZED STATISTICS OF INDISTIGUISHABLE PARTI-
CLES 1
1.1 The Symmetrization Postulate 1
1.2 Identicality and Indistinguishability 2
1.3 The Quantum Statistics of Indistinguishable Particles 5
1.4 Cluster Decomposition: Systems and Subsystems 7
1.5 Conclusion 8
2 STATISTICAL MECHANICS OF IDENTICAL PARTICLES 9
2.1 Multiparticle States and the Permutation Group 9
2.1.1 Notation and Fimdamentals 10
2.1.2 Frobenius Symbols 10
2.2 Partition Fvmctions for (In)distinguishable Particles 12
2.2.1 Parabosons and Parafermions 19
2.2.2 Beyond Parabosons and Parafermions 28
2.3 Degenerate Systems 35
2.4 Conclusion 37
3 STATISTICAL MECHANICS OF EXTENSIVE SYSTEMS 39
3.1 Extensivity 39
3.2 Extensivity and Positive Counting 41
3.3 Classification 45
3.4 Symmetry Types in Fuzzy Statistics 47
3.5 Examples and Comparisons 50
3.5.1 Interpolating Between Bosons and Fermions 50
3.5.2 Haldane/Wu and Polychronakos's Fractional Statistics 52
3.5.3 Gentile Statistics 54
3.6 Conclusion 56
4 SECOND QUANTIZATION AND GENERALIZED STATISTICS 57
4.1 Algebras: Bilinear and Trilinear Relations 58
4.2 Actions of the Permutation Groups 63
4.2.1 Gram Matrices and the Representations of the Permutation
Group 67
4.2.2 Clustering Revisited 81
4.3 Classification 85
4.3.1 Examples 90
4.4 Known Models 95
4.4.1 Green's Parastatistics 95
4.4.2 Greenberg's Quons 96
4.4.3 Meljanac's proposal and Govorkov's Parastatistics 96
4.5 Conclusion 98
5 ENSCRIPTION AND TRANSLATION OF QUANTUM TEXTS . 100
5.1 Cloning and Quantum Information 100
5.2 Enscription 104
5.3 Enscribing 2-texts 113
5.4 Enscribing Real-Uniform N-texts 116
5.4.1 Real-Uniform 3-Texts 119
5.4.2 Real-Uniform N-Texts 128
5.5 The Structure of an Enscribable Text 133
5.6 Enscription as a Resource: Probabilistic Clorung 135
5.7 Translation 142
5.8 Graphs and the Structure of Translatable Texts 145
CITED LITERATURE 162
