Quantum Mechanics associated with a Finite Group
| dc.creator | Johnson, Robert W. | |
| dc.date | 2006-04-20 | |
| dc.date.accessioned | 2026-07-07T07:11:54Z | |
| dc.date.available | 2026-07-07T07:11:54Z | |
| dc.description | 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. | |
| dc.description | Submitted to Intern. J. Theor. Phys | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0604153 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0604153 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111938 | |
| dc.subject | Quantum Physics | |
| dc.title | Quantum Mechanics associated with a Finite Group | |
| dc.type | text |