On gauge invariance and the path integral

TL;DR

This paper derives the path integral formulation for a charged particle in a stationary magnetic field using a gauge covariant operator approach, confirming the midpoint rule for discretized interaction terms.

Contribution

It introduces a gauge covariant operator method to derive the path integral and verifies the midpoint rule in this context.

Findings

Path integral for a charged particle in a magnetic field is derived.

Midpoint rule for the interaction term is confirmed.

Gauge covariance is maintained throughout the derivation.

Abstract

Using a gauge covariant operator technique we deduce the path integral for a charged particle in a stationary magnetic field, verifying the "midpoint rule" for the discrete form of the interaction term with the vector potential.