Path algebras, wave-particle duality, and quantization of phase space
Abstract
Semigroup algebras admit certain `coherent' deformations which, in the special case of a path algebra, may associate a periodic function to an evolving path; for a particle moving freely on a straight line after an initial impulse, the wave length is that hypothesized by de Broglie's wave-particle duality. This theory leads to a model of "physical" phase space of which mathematical phase space, the cotangent bundle of configuration space, is a projection. This space is singular, quantized at the Planck level, its structure implies the existence of spin, and the spread of a packet can be described as a random walk. The wavelength associated to a particle moving in this space need not be constant and its phase can change discontinuously.
Cite
@article{arxiv.1505.05859,
title = {Path algebras, wave-particle duality, and quantization of phase space},
author = {Murray Gerstenhaber},
journal= {arXiv preprint arXiv:1505.05859},
year = {2016}
}
Comments
15 pages, replaces arXiv1505.0589; to appear Letters in Mathematical Physics