Abstract
We show that defining the observed proper velocity and acceleration of a spin zero particle as the first and second derivatives of the classical expectation value for the space-time position vector, defined on a manifold carrying the Lorentz metric, with respect to a conditioning parameter τ, yields directly: a Lorentz and gauge invariant quantum mechanics, the Lorentz force, Maxwell's equations and a field equation for a non-electromagnetic potential. This also provides a new basis for gauge conditions in the field theory and shows that only the Lorentz gauge condition is admissible in electromagnetic theory.
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Collins, R.E. The mathematical basis of physical laws: Relativistic mechanics, quantum mechanics, the Lorentz force, Maxwell's equations and non-electromagnetic forces for spin zero particles. Found Phys Lett 7, 39–58 (1994). https://doi.org/10.1007/BF02056551
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DOI: https://doi.org/10.1007/BF02056551