Gauge transformation through an accelerated frame of reference

TL;DR

This paper demonstrates that gauge transformations in quantum mechanics can be equivalently represented by extended Galilean transformations between accelerating reference frames, linking gauge symmetry with frame acceleration effects.

Contribution

It reveals a novel connection between gauge transformations and extended Galilean transformations, providing a new perspective on gauge symmetry in quantum systems.

Findings

Gauge transformation effects can be mimicked by extended Galilean transformations.

Wave-function phase factors relate to frame acceleration.

Provides a unified view of gauge and frame transformations.

Abstract

The Schr\"{o}dinger equation of a charged particle in a uniform electric field can be specified in either a time-independent or a time-dependent gauge. The wave-function solutions in these two gauges are related by a phase-factor reflecting the gauge symmetry of the problem. In this article we show that the effect of such a gauge transformation connecting the two wave-functions can be mimicked by the effect of two successive extended Galilean transformations connecting the two wave-function. An extended Galilean transformation connects two reference frames out of which one is accelerating with respect to the other.