|
| related topics |
| {group, space, representation} |
| {equation, function, exp} |
| {operator, operators, space} |
| {measurement, state, measurements} |
| {field, particle, equation} |
|
Quantum Mechanics associated with a Finite Group
Robert W. Johnson
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0604153
- categories:
- quant-ph
- comments:
- Submitted to Intern. J. Theor. Phys
- arxiv_id:
- quant-ph/0604153
- created:
- 2006-04-20
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