We usually describe the set by a

gauge transformation that joins each subclass.

As a result, in order to get a symmetric EMEM tensor for a system with charges, the corresponding gauge transformation (3) should be based on Eq.

In the next Section we will consider this particular case implying accelerations of all charged particles as negligible and will show that the corresponding EMEM tensor (8) can be subjected to an appropriate gauge transformation, which allows elimination of the divergent terms in its structure and logically brings into the absence of bound EM field retardation within the near zone.

The request of invariance of the Maxwell equations for possible transformations of the aforementioned potentials addresses gauge transformations.

9) are invariant with respect to the gauge transformations (2.

Thus, Maxwell's equations are also invariant under these gauge transformations.

In the present paper, we have introduced new gauge transformations that leave Maxwell's equations, Lorentz gauge and the continuity equations invariant.

k] through local phase changes, we recall that the electromagnetic field is the gauge field which guarantees invariance of the Lagrangian density under space-time local U(1) gauge transformations, i.

It is the gauge field which guarantees invariance under space-local U(1) gauge transformations.

Let us do a calculus of variation on this integral to derive a variational equation by applying a gauge transformation on (24) as follows.

Under a gauge transformation (regarded as a change of coordinate) with gauge function a(z(s)) this coordinate is changed to another coordinate ([A'.

These transformations are similar to

gauge transformations endorse on the vector potential ([?