%0 Journal Article
%T Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence
%A Gustavo V. L¨®pez
%A Jorge A. Lizarraga
%J Journal of Modern Physics
%P 474-479
%@ 2153-120X
%D 2024
%I Scientific Research Publishing
%R 10.4236/jmp.2024.154022
%X 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 <strong><em>B</em></strong> and its vector potential &nbsp;<em><strong>A</strong></em>, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that <strong><em>B</em>=</strong><span style=\"white-space:nowrap;\"><strong>&amp;#8711;</strong></span><span style=\"white-space:nowrap;\"><strong>&amp;#215;</strong></span><strong></strong><strong><em>A</em>&nbsp;</strong>if and only if <strong><em>B</em></strong><span style=\"white-space:nowrap;\"><strong>&amp;#8800;</strong></span><strong>0</strong>.
%K Gauge Transformation
%K Harmonic Oscillator
%K Quantum Hall Effect
%K Electromagnetic Potentials
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=132080