Why semiclassical electrodynamics is not gauge invariant

A. M. Stewart

doi:10.1088/0305-4470/33/50/303

Why semiclassical electrodynamics is not gauge invariant

A. M. Stewart^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

It is shown that in semiclassical electrodynamics, which describes how electrically charged particles move according to the laws of quantum mechanics under the influence of a prescribed classical electromagnetic field, only a restricted class of gauge transformations is allowed. This lack of full gauge invariance, in contrast to the situation in classical and quantum electrodynamics which are fully gauge-invariant theories, is due to the requirement that the scalar potential in the Hamiltonian of wave mechanics should represent a physical potential. Probability amplitudes and energy differences are independent of gauge within this restricted class of gauge transformation.

Original language	English
Pages (from-to)	9165-9176
Number of pages	12
Journal	Journal of Physics A: Mathematical and General
Volume	33
Issue number	50
DOIs	https://doi.org/10.1088/0305-4470/33/50/303
Publication status	Published - 22 Dec 2000

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AB - It is shown that in semiclassical electrodynamics, which describes how electrically charged particles move according to the laws of quantum mechanics under the influence of a prescribed classical electromagnetic field, only a restricted class of gauge transformations is allowed. This lack of full gauge invariance, in contrast to the situation in classical and quantum electrodynamics which are fully gauge-invariant theories, is due to the requirement that the scalar potential in the Hamiltonian of wave mechanics should represent a physical potential. Probability amplitudes and energy differences are independent of gauge within this restricted class of gauge transformation.

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Why semiclassical electrodynamics is not gauge invariant

Abstract

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