dorsal/arxiv
View SchemaQuantum Mechanics associated with a Finite Group
| Authors | Robert W. Johnson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604153 |
| URL | https://arxiv.org/abs/quant-ph/0604153 |
Abstract
I describe, in the simplified context of finite groups and their representations, a mathematical model for a physical system that contains both its quantum and classical aspects. The physically observable system is associated with the space containing elements fxf for f an element in the regular representation of a given finite group G. The Hermitian portion of fxf is the Wigner distribution of f whose convolution with a test function leads to a mathematical description of the quantum measurement process. Starting with the Jacobi group that is formed from the semidirect product of the Heisenberg group with its automorphism group SL(2,F{N}) for N an odd prime number I show that the classical phase space is the first order term in a series of subspaces of the Hermitian portion of fxf that are stable under SL(2,F{N}). I define a derivative that is analogous to a pseudodifferential operator to enable a treatment that parallels the continuum case. I give a new derivation of the Schrodinger-Weil representation of the Jacobi group. Keywords: quantum mechanics, finite group, metaplectic. PACS: 03.65.Fd; 02.10.De; 03.65.Ta.
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"abstract": "I describe, in the simplified context of finite groups and their\nrepresentations, a mathematical model for a physical system that contains both\nits quantum and classical aspects. The physically observable system is\nassociated with the space containing elements fxf for f an element in the\nregular representation of a given finite group G. The Hermitian portion of fxf\nis the Wigner distribution of f whose convolution with a test function leads to\na mathematical description of the quantum measurement process. Starting with\nthe Jacobi group that is formed from the semidirect product of the Heisenberg\ngroup with its automorphism group SL(2,F{N}) for N an odd prime number I show\nthat the classical phase space is the first order term in a series of subspaces\nof the Hermitian portion of fxf that are stable under SL(2,F{N}). I define a\nderivative that is analogous to a pseudodifferential operator to enable a\ntreatment that parallels the continuum case. I give a new derivation of the\nSchrodinger-Weil representation of the Jacobi group. Keywords: quantum\nmechanics, finite group, metaplectic. PACS: 03.65.Fd; 02.10.De; 03.65.Ta.",
"arxiv_id": "quant-ph/0604153",
"authors": [
"Robert W. Johnson"
],
"categories": [
"quant-ph"
],
"title": "Quantum Mechanics associated with a Finite Group",
"url": "https://arxiv.org/abs/quant-ph/0604153"
},
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