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arXiv · 1505.05859

Path algebras, wave-particle duality, and quantization of phase space

Murray Gerstenhaber
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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.

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Murray Gerstenhaber. 2016-10-02. Path algebras, wave-particle duality, and quantization of phase space. https://doi.org/10.1007/s11005-016-0909-8

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