Internal gauge space electrodynamics

The group space of 0(3) is doubly connected (i.e., non-simply connected) and can therefore support an Aharonov-Bohm effect (Section V), which is described by a physical inhomogeneous term produced by a rotation in the internal gauge space of 0(3) [24]. The existence of the Aharonov-Bohm effect is therefore clear evidence for an extended electrodynamics such as 0(3) electrodynamics, as argued already. A great deal more evidence is reviewed in this article in favor of 0(3) over U(l). For example, it is shown that the Sagnac effect [25] can be described accurately with 0(3), while U(l) fails completely to describe it. 

Information is also lost if we replace the ((1),(2),(3)) basis by the (X, Y, Z) basis for the internal gauge space. The reason is that the former basis is essentially dynamical and the latter is essentially static. This is again a self-consistent result, because electrodynamics, by definition, requires the movement of charge. The misnamed subject of magnetostatics also requires the movement of charge, and so is not static. 

This is an expression for the observed phase difference with the platform at rest in the Sagnac experiment [47] it is a rotation in the internal gauge space. In U(l) electrodynamics, there is no phase difference when the platform is at rest, as discussed already. 

The principle of interferometry in 0(3) electrodynamics follows from the fact that it is caused by a rotation in the internal gauge space... 

The explanation of the IFE in the Maxwell-Heaviside theory relies on phenomenology that is self-inconsistent. The reason is that A x A 2 is introduced phenomenologically [56] but the same quantity (Section III) is discarded in U(l) gauge field theory, which is asserted in the received view to be the Maxwell-Heaviside theory. In 0(3) electrodynamics, the IFE and third Stokes parameter are both manifestations of the 3 held proportional to the conjugate product that emerges from first principles [11-20] of gauge held theory, provided the internal gauge space is described in the basis ((1),(2),(3)). 

A closely similar complex circular basis has been described by Silver [112] for three-dimensional space. This space forms the internal gauge space in 0(3) electrodynamics, as argued already. In the complex circular basis, the unit vector dot product is... 

This means that a magnetic field is always a quantity that depends on motion, or a current. If there is no magnetic field, there is no electric current, that is, no motion of charge. The use of Cartesian indices for the internal 0(3) gauge space therefore corresponds to an electrostatic situation where there is no movement of charge. The use of complex circular indices corresponds to electrodynamics. 

As we have argued, the basis ((1),(2),(3)) defines an internal space in electrodynamics, and was first applied as such by Barrett [50] in an SU(2) invariant gauge theory. As a consequence of this hypothesis, we can write... 

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