Author(s)

Gustavo V. López^*, Jorge A. Lizarraga

Departamento de Física, Universidad de Guadalajara, Guadalajara, Mexico.

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.

Gauge Transformation, Harmonic Oscillator, Quantum Hall Effect, Electromagnetic Potentials

López, G. and Lizarraga, J. (2024) Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence. Journal of Modern Physics, 15, 474-479. doi: 10.4236/jmp.2024.154022.