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Path algebras, wave-particle duality, and quantization of phase space
- 作者:Murray Gerstenhaber
- 关键词:Cohomology ; Deformation ; Homotopy ; Semigroups
- 刊名:Letters in Mathematical Physics
- 出版年:2017
- 出版时间:March 2017
- 年:2017
- 卷:107
- 期:3
- 页码:409-426
- 全文大小:
- 刊物类别:Physics and Astronomy
- 刊物主题:Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations;
- 出版者:Springer Netherlands
- ISSN:1573-0530
- 卷排序:107
文摘
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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