Gauge field theory

Therefore, this is a statement of our fundamental hypothesis, specifically, that the topology of the vacuum defines the field equations through group and gauge field theory. Prior to the inference and empirical verification of the Aharonov-Bohm effect, there was no such concept in classical electrodynamics, the ether having been denied by Lorentz, Poincare, Einstein, and others. Our development of 0(3) electrodynamics in this chapter, therefore, has a well-defined basis in fundamental topology and empirical data. In the course of the development of... 

In summary of this introduction therefore, we develop a novel theory of electrodynamics based on vacuum topology that gives self-consistent descriptions of empirical data where an electrodynamics based on a U(l) vacuum fails. It turns out that 0(3) electrodynamics does not incorporate a monopole, as a material point particle, because it is a theory based on the topology of the vacuum. The next section provides foundational justification for gauge field theory using fiber bundle theory. 

A simple example in classical electrodynamics of what is now known as gauge invariance was introduced by Heaviside [3,4], who reduced the original electrodynamical equations of Maxwell to their present form. Therefore, these equations are more properly known as the Maxwell-Heaviside equations and, in the terminology of contemporary gauge field theory, are identifiable as U(l) Yang-Mills equations [15]. The subj ect of this chapter is 0(3) Yang-Mills gauge theory applied to electrodynamics and electroweak theory. 

In general gauge field theory [6], the field tensor is proportional to the commutator of variant derivatives. This is the result of a round trip or closed... 

This result is inconsistent with the fact that the differential equation developed by Heaviside from Maxwell s original equations describe circular polarization. The root of the inconsistency is that U(l) gauge field theory is made to correspond with Maxwell-Heaviside theory by discarding the commutator Am x A(2). The neglect of the latter results in a reduction to absurdity, because if S3 vanishes, so does the zero order Stokes parameter ... 

Recall that in general gauge field theory, for any gauge group, the field tensor is defined through the commutator of covariant derivatives. In condensed notation [6]... 

The Maxwell-Heaviside theory seen as a U(l) symmetry gauge field theory has no explanation for the photoelectric effect, which is the emission of electrons from metals on ultraviolet irradiation [39]. Above a threshold frequency, the emission is instantaneous and independent of radiation intensity. Below the threshold, there is no emission, however intense the radiation. In U(l), electrodynamics energy is proportional to intensity and there is, consequently, no possible explanation for the photoelectric effect, which is conventionally regarded as an archetypical quantum effect. In classical 0(3) electrodynamics, the effect is simply... 

The Lehnert field equations in the vacuum also exist in U(l) form, and were originally postulated [7-10] in U(l) gauge field theory. It can be demonstrated as follows, that they originate from the U(l) gauge field equations when matter is not present ... 

In order to understand interferometry at a fundamental level in gauge field theory, the starting point must be the non-Abelian Stokes theorem [4]. The theorem is generated by a round trip or closed loop in Minkowski spacetime using covariant derivatives, and in its most general form is given [17] by... 

The IFE was inferred phenomenologically by Pershan [56] in terms of the conjugate product of circularly polarized electric fields, E x E = Em X e 2). In 0(3) electrodynamics, it is described from the first principles of gauge field theory by the inhomogeneous field equation (32), which can be expanded as... 

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)). 

The expression equivalent to Eq. (68) in general gauge field theory is [11]... 

The equivalent equation in general gauge field theory is... 

We reconsider both items 1 and 2 on the basis of more modem developments in particle physics and gauge field theory well after the foundations of electrodynamics were set by Maxwell. Self-powering systems readily extracting electrical energy from the vacuum to power themselves and their loads can be quickly developed whenever the scientific community will permit their research and development to be funded. 

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