Abstract
A new approach to developing formulisms of physics based solely on laws of mathematics is presented. From simple, classical statistical definitions for the observed space-time position and proper velocity of a particle having a discrete spectrum of internal states we derive u generalized Schrödinger equation on the space-time manifold. This governs the evolution of an N component wave function with each component square integrable over this manifold and is structured like that for a charged particle in an electromagnetic field but also includes SU(N) gauge field couplings. This construction reveals a new hasis for gauge invariance and new insight into the appearance of spin and other such properties in relativistic quantum mechanics and suggests a new charged particle model.
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Collins, R.E. Differentiable probabilities: A new viewpoint on spin, gauge invariance, gauge fields, and relativistic quantum mechanics. Found Phys 26, 1469–1527 (1996). https://doi.org/10.1007/BF02272368
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DOI: https://doi.org/10.1007/BF02272368