Journal of Modern Physics

Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence

Gustavo V. López, Jorge A. Lizarraga

Published Jan 1, 2024• 0 citations

Abstract

Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.

DOI: 10.4236/jmp.2024.154022

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