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Wave mechanics without gauge fixing

A. M. Stewart
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Abstract

By using the multipolar gauge it is shown that the quantum mechanics of an electrically charged particle moving in a prescribed classical electromagnetic field (wave mechanics) may be expressed in a manner that is gauge invariant, except that the only gauge functions that are allowable in a gauge transformation are those that consist of the sum of a function that depends only on the space coordinates and a term that is the product of a constant and the time coordinate. The multipolar gauge specifies the specific set of potentials that are best suited for use in the Schroedinger equation.

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A. M. Stewart. 2005-05-11. Wave mechanics without gauge fixing. https://arxiv.org/abs/quant-ph/0505079

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