dorsal/arxiv
View SchemaIdentity, Geometry, Permutation And The Spin-Statistics Theorem
| Authors | Michael J. York |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9908078 |
| URL | https://arxiv.org/abs/quant-ph/9908078 |
Abstract
We examine historic formulations of the spin-statistics theorem from a point of view that distinguishes between the observable consequences and the ``symmetrization postulate''. In particular, we make a critical analysis of concepts of particle identity, state distinguishability and permutation, and particle ``labels''. We discuss how to construct unique state vectors and the nature of the full state descriptions required for this -- in particular the elimination of arbitrary $2\pi$ rotations on fermion spin quantization frames and argue that the failure to do this renders the conventional symmetrization postulate (and previous ``proofs'' of it) at best {\em incomplete}. We discuss particle permutation in a general way for any pairs of particles, whether identical or not, and make an essential distinction between exchange and pure permutation. We prove a revised symmetrization postulate that allows us to construct state vectors that are naturally symmetric under pure permutation, {\em for any spin}. The significance of particle labels (which, in the exchange operation, are not permuted along with other variables) is then that they stand in for any asymmetry (order dependence) that is present in the full state descriptions necessary for unique state vectors but not explicit in the regular state variables. {\em The exchange operation is then the physical transformation that reverses any asymmetry implicit in the labels}. We point out a previously unremarked geometrical asymmetry between all pairs of particles that is present whenever we choose a common frame of reference. We compute the exchange phase for various state vectors using different spin quantization frames, and prove the Pauli Exclusion Principle and its generalization to arbitrary spin.
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"abstract": "We examine historic formulations of the spin-statistics theorem from a point\nof view that distinguishes between the observable consequences and the\n``symmetrization postulate\u0027\u0027. In particular, we make a critical analysis of\nconcepts of particle identity, state distinguishability and permutation, and\nparticle ``labels\u0027\u0027. We discuss how to construct unique state vectors and the\nnature of the full state descriptions required for this -- in particular the\nelimination of arbitrary $2\\pi$ rotations on fermion spin quantization frames\nand argue that the failure to do this renders the conventional symmetrization\npostulate (and previous ``proofs\u0027\u0027 of it) at best {\\em incomplete}.\n We discuss particle permutation in a general way for any pairs of particles,\nwhether identical or not, and make an essential distinction between exchange\nand pure permutation. We prove a revised symmetrization postulate that allows\nus to construct state vectors that are naturally symmetric under pure\npermutation, {\\em for any spin}. The significance of particle labels (which, in\nthe exchange operation, are not permuted along with other variables) is then\nthat they stand in for any asymmetry (order dependence) that is present in the\nfull state descriptions necessary for unique state vectors but not explicit in\nthe regular state variables. {\\em The exchange operation is then the physical\ntransformation that reverses any asymmetry implicit in the labels}.\n We point out a previously unremarked geometrical asymmetry between all pairs\nof particles that is present whenever we choose a common frame of reference. We\ncompute the exchange phase for various state vectors using different spin\nquantization frames, and prove the Pauli Exclusion Principle and its\ngeneralization to arbitrary spin.",
"arxiv_id": "quant-ph/9908078",
"authors": [
"Michael J. York"
],
"categories": [
"quant-ph",
"hep-th",
"physics.ed-ph"
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"title": "Identity, Geometry, Permutation And The Spin-Statistics Theorem",
"url": "https://arxiv.org/abs/quant-ph/9908078"
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