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Bohm, A., Mostafazadeh, A., Koizumi, H., Niu, Q. and Zwanziger, J. (2003) The Geometric Phase in Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics. Springer, Berlin.
https://doi.org/10.1007/978-3-662-10333-3

has been cited by the following article:

• TITLE: Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence

  AUTHORS: Gustavo V. López, Jorge A. Lizarraga

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

  JOURNAL NAME: Journal of Modern Physics, Vol.15 No.4, March 28, 2024

  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=∇×Aif and only if B≠0.