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The theory of electrodynamics can be cast into biquaternion form. Usually Maxwell's equations are invariant with respect to a gauge transformation of the potentials and one can choose freely a gauge condition. For instance, the Lorentz gauge condition yields the potential Lorenz inhomogeneous wave equations such that the generalized Maxwell theory, expressed in terms of the potentials, automatically satisfy the Lorenz inhomogeneous wave equations, without any gauge condition. This theory of electrodynamics is no longer gauge invariant with respect to a transformation of the potentials: it is electrodynamics with broken gauge symmetry. The appearance of the extra scalar field terms can be described as a conditional current regauge that does not violate the conservation of charge, and it has several consequences: the prediction of a longitudinal electroscalar wave (LES wave) in vacuum; superluminal wave solutions, and possibly classical theory about photon tunneling; a generalized Lorentz force expression that contains an extra scalar term; generalized energy and momentum theorems, with an extra power flow term associated with LES waves. A charge density wave that only induces a scalar field is possible in this theory.
For more information please see "Electrodynamics with a Scalar Field". |
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Publication reference: Koen J. van Vlaenderen and André Waser, Hadronic Journal 24 ( 2001) 609-628 |
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