dorsal/arxiv
View SchemaSpin-Statistics Theorem and Geometric Quantisation
| Authors | Charis Anastopoulos |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0110169 |
| URL | https://arxiv.org/abs/quant-ph/0110169 |
| DOI | 10.1142/S0217751X04017860 |
| Journal | Int.J.Mod.Phys.A19:655-676,2004 |
Abstract
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the non-relativistic domain (in fact for any symmetry group including internal symmetries) without quantum field theory, by the requirement that the exchange can be implemented smoothly by a class of symmetry transformations that project in the phase space of the joint system. We discuss the interpretation of this requirement, stressing the fact that any distinction of identical particles comes solely from the choice of coordinates. We then examine our construction in the geometric and the coherent-state-path-integral quantisation schemes. In the appendix we apply our results to exotic systems exhibiting continuous ``spin'' and ``fractional statistics''. This gives novel and unusual forms of the spin-statistics relation.
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"abstract": "We study how the spin-statistics theorem relates to the geometric structures\non phase space that are introduced in quantisation procedures (namely a U(1)\nbundle and connection). The relation can be proved in both the relativistic and\nthe non-relativistic domain (in fact for any symmetry group including internal\nsymmetries) without quantum field theory, by the requirement that the exchange\ncan be implemented smoothly by a class of symmetry transformations that project\nin the phase space of the joint system. We discuss the interpretation of this\nrequirement, stressing the fact that any distinction of identical particles\ncomes solely from the choice of coordinates. We then examine our construction\nin the geometric and the coherent-state-path-integral quantisation schemes. In\nthe appendix we apply our results to exotic systems exhibiting continuous\n``spin\u0027\u0027 and ``fractional statistics\u0027\u0027. This gives novel and unusual forms of\nthe spin-statistics relation.",
"arxiv_id": "quant-ph/0110169",
"authors": [
"Charis Anastopoulos"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1142/S0217751X04017860",
"journal_ref": "Int.J.Mod.Phys.A19:655-676,2004",
"title": "Spin-Statistics Theorem and Geometric Quantisation",
"url": "https://arxiv.org/abs/quant-ph/0110169"
},
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