Path algebras and de Broglie waves
Mathematical Physics
2014-03-17 v1 Algebraic Topology
math.MP
Quantum Algebra
Rings and Algebras
Abstract
De Broglie waves may be a reflection of a deformation inherent in the path algebra of phase space. On a Riemannian manifold equipped with a suitable 2-form, the product of paths, which is ordinarily their concatenation, can be deformed by multiplication by a scalar weight giving rise to a function on paths. In flat phase space the associated function is periodic with period the de Broglie wave length. The de Broglie description may only be approximate in curved space.
Cite
@article{arxiv.1403.3429,
title = {Path algebras and de Broglie waves},
author = {Murray Gerstenhaber},
journal= {arXiv preprint arXiv:1403.3429},
year = {2014}
}
Comments
13 pages. arXiv admin note: substantial text overlap with arXiv:1306.4939