Yang-Mills theory 0 electrodynamics

There exist generally covariant four-valued 4-vectors that are components of q, and these can be used to construct the basic structure of 0(3) electrodynamics in terms of single-valued components of the quaternion-valued metric q1. Therefore, the Sachs theory can be reduced to 0(3) electrodynamics, which is a Yang-Mills theory [3,4]. The empirical evidence available for both the Sachs and 0(3) theories is summarized in this review, and discussed more extensively in the individual reviews by Sachs [1] and Evans [2]. In other words, empirical evidence is given of the instances where the Maxwell-Heaviside theory fails and where the Sachs and 0(3) electrodynamics succeed in describing empirical data from various sources. The fusion of the 0(3) and Sachs theories provides proof that the B(3) held [2] is a physical held of curved spacetime, which vanishes in hat spacetime (Maxwell-Heaviside theory [2]). 

In Eq. (5), the product q q is quaternion-valued and non-commutative, but not antisymmetric in the indices p and v. The B<3> held and structure of 0(3) electrodynamics must be found from a special case of Eq. (5) showing that 0(3) electrodynamics is a Yang-Mills theory and also a theory of general relativity [1]. The important conclusion reached is that Yang-Mills theories can be derived from the irreducible representations of the Einstein group. This result is consistent with the fact that all theories of physics must be theories of general relativity in principle. From Eq. (1), it is possible to write four-valued, generally covariant, components such as... 

Since 0(3) electrodynamics is a Yang-Mills theory [3,4], we can write... 

All topological theories are nonlinear, a feature of both the Sachs and Evans theories, and the whole of quantum theory can be replaced by topology [1], which reduces in some circumstances to the Yang-Mills theory [1], of which 0(3) electrodynamics [3] is an example. 0(3) electrodynamics has been developed into an 0(3) symmetry quantum field theory by Evans and Crowell... 

There are therefore obvious points of similarity between the 0(3) theory of electrodynamics and the Yang-Mills theory [44], Both are based, as we have argued, on an 0(3) or SU(2) invariant Lagrangian. However, in 0(3) electrodynamics, the particle concomitant with the field has the topological charge k/A(0>. In 0(3) electrodynamics, the internal space and spacetime are not independent spaces but form an extended Lie algebra [42], In elementary particle... 

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. 

From the foregoing, U(l) electrodynamics was never a complete theory, although it is rigidly adhered to in the received view. It has been argued already that the Maxwell-Heaviside theory is a U(l) Yang-Mills gauge theory that discards the basic commutator A(1) x A(2). However, this commutator appears in the fundamental definition of circular polarity in the Maxwell-Heaviside theory through the third Stokes parameter... 

The 0(3) electrodynamics developed by Evans [2], and its homomorph, the SU(2) electrodynamics of Barrett [10], are substructures of the Sachs theory dependent on a particular choice of metric. Both 0(3) and SU(2) electrodynamics are Yang-Mills structures with a Wu-Yang phase factor, as discussed by Evans and others [2,9]. Using the choice of metric (17), the electromagnetic energy density present in the 0(3) curved spacetime is given by the product... 

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