dorsal/arxiv
View SchemaSpatial Asymmetry For Particle Pairs And The Spin-Statistics Theorem
| Authors | Michael J. York |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9809012 |
| URL | https://arxiv.org/abs/quant-ph/9809012 |
Abstract
We discuss the conditions under which identical particles may yet be distinguishable and the relationship between particle permutation and exchange. We show that we can always define permutation-symmetric state vectors. When the particles are completely indistinguishable, then exchange is equivalent to permutation and therefore the exchange eigenvalue for such permutation-symmetric state vectors is always +1. Exchange asymmetry arises when the particles are physically distinguishable, even though otherwise identical, and can be computed from the transformations that arise when the distinguishing features are reversed. There is a fundamental spatial asymmetry between the relative orientations of any two vectors in a common frame of reference that persists even in the limit that the vectors coincide. For a pair of particles this asymmetry between their spin quantization frames renders them distinguishable even when otherwise identical. In the conventional construction, this distinction is not properly accounted for. Particle exchange is then equivalent to reversing this relative orientation --- which requires a relative rotation by 2pi on the spin quantization frame of one particle with respect to the other, thus resulting in the conventional exchange phase.
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"abstract": "We discuss the conditions under which identical particles may yet be\ndistinguishable and the relationship between particle permutation and exchange.\nWe show that we can always define permutation-symmetric state vectors. When the\nparticles are completely indistinguishable, then exchange is equivalent to\npermutation and therefore the exchange eigenvalue for such\npermutation-symmetric state vectors is always +1. Exchange asymmetry arises\nwhen the particles are physically distinguishable, even though otherwise\nidentical, and can be computed from the transformations that arise when the\ndistinguishing features are reversed.\n There is a fundamental spatial asymmetry between the relative orientations of\nany two vectors in a common frame of reference that persists even in the limit\nthat the vectors coincide. For a pair of particles this asymmetry between their\nspin quantization frames renders them distinguishable even when otherwise\nidentical. In the conventional construction, this distinction is not properly\naccounted for. Particle exchange is then equivalent to reversing this relative\norientation --- which requires a relative rotation by 2pi on the spin\nquantization frame of one particle with respect to the other, thus resulting in\nthe conventional exchange phase.",
"arxiv_id": "quant-ph/9809012",
"authors": [
"Michael J. York"
],
"categories": [
"quant-ph"
],
"title": "Spatial Asymmetry For Particle Pairs And The Spin-Statistics Theorem",
"url": "https://arxiv.org/abs/quant-ph/9809012"
},
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