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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.
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
We derive the Landau-Khalatnikov-Frandkin transformation (LKFT) for the fermion propagator in quantum electrodynamics (QED) described within a brane-world inspired framework where photons are allowed to move in $d_gamma$ space-time (bulk) dimensions,
The time evolution of a charged point particle is governed by a second-order integro-differential equation that exhibits advanced effects, in which the particle responds to an external force before the force is applied. In this paper we give a simple
If a tennis ball is held above a basket ball with their centers vertically aligned, and the balls are released to collide with the floor, the tennis ball may rebound at a surprisingly high speed. We show in this article that the simple textbook expla
The instantaneous nature of the potentials of the Coulomb gauge is clarified and a concise derivation is given of the vector potential of the Coulomb gauge expressed in terms of the instantaneous magnetic field.