dorsal/arxiv
View SchemaSuperselection from canonical constraints
| Authors | Michael J. W. Hall |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404123 |
| URL | https://arxiv.org/abs/quant-ph/0404123 |
| DOI | 10.1088/0305-4470/37/31/011 |
| Journal | J.Phys. A37 (2004) 7799-7812 |
Abstract
The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course, equivalent to the Schroedinger equation for the wavefunction, which is linear. However, quite simple constraints on the canonical fields P and S correspond to_nonlinear_ constraints on the wavefunction. Such constraints act to prevent certain superpositions of wavefunctions from being realised, leading to superselection-type rules. Examples leading to superselection for energy, spin-direction and `classicality' are given. The canonical formulation of the equations of motion, in terms of a probability density and its conjugate, provides a universal language for describing classical and quantum ensembles on both continuous and discrete configuration spaces, and is briefly reviewed in an appendix.
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"abstract": "The evolution of both quantum and classical ensembles may be described via\nthe probability density P on configuration space, its canonical conjugate S,\nand an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is,\nof course, equivalent to the Schroedinger equation for the wavefunction, which\nis linear. However, quite simple constraints on the canonical fields P and S\ncorrespond to_nonlinear_ constraints on the wavefunction. Such constraints act\nto prevent certain superpositions of wavefunctions from being realised, leading\nto superselection-type rules. Examples leading to superselection for energy,\nspin-direction and `classicality\u0027 are given. The canonical formulation of the\nequations of motion, in terms of a probability density and its conjugate,\nprovides a universal language for describing classical and quantum ensembles on\nboth continuous and discrete configuration spaces, and is briefly reviewed in\nan appendix.",
"arxiv_id": "quant-ph/0404123",
"authors": [
"Michael J. W. Hall"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1088/0305-4470/37/31/011",
"journal_ref": "J.Phys. A37 (2004) 7799-7812",
"title": "Superselection from canonical constraints",
"url": "https://arxiv.org/abs/quant-ph/0404123"
},
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