Physics – Quantum Physics
Scientific paper
2006-04-20
Physics
Quantum Physics
Submitted to Intern. J. Theor. Phys
Scientific paper
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.
No associations
LandOfFree
Quantum Mechanics associated with a Finite Group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum Mechanics associated with a Finite Group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Mechanics associated with a Finite Group will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-67278