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Register a new userStrong limitations on allowable gauge transformations in electrodynamics
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Authors
H. R. Reiss
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Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine dynamics, and electromagnetic forces depend directly on fields. However, physical conservation principles come from symmetries such as those following from Noethers theorem, and these require potentials for their statement. Examples are given of potentials that describe fields correctly but that violate conservation principles, demonstrating that the correct statement of potentials is necessary. An important consequence is that gauge transformations are severely limited when conservation conditions must be satisfied. When transverse and longitudinal fields are present concurrently, the only practical gauge is the radiation gauge.
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Gauge invariance, a core principle in electrodynamics, has two separate meanings, only one of which is robust. The reliable concept treats the photon as the gauge field for electrodynamics. It is based on symmetries of the Lagrangian, and requires no mention of electric or magnetic fields. The other depends directly on the electric and magnetic fields, and how they can be represented by potential functions that are not unique. The first gauge concept has been fruitful, whereas the second has the defect that there exist gauge transformations from physical to unphysical states. The fields are unchanged by the gauge transformation, so that potentials are the necessary guides to correctness.
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