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arXiv · 1403.3429

Path algebras and de Broglie waves

Murray Gerstenhaber
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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.

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Murray Gerstenhaber. 2014-03-13. Path algebras and de Broglie waves. https://arxiv.org/abs/1403.3429

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