Scalar electrodynamics

In refs (Kim,2004 Kim, 2005) we take one step further estimating corrections to the Gaussian effective potential for the U(l) scalar electrodynamics where it represents the standard static GL effective model of superconductivity. Although it was found that, in the covariant pure (f)4 theory in 3 + 1 dimensions,corrections to the GEP are not large (Stancu,1990), we do not expect them to be negligible in three dimensions for high Tc superconductivity, where the system is strongly correlated. 

Nearly two years ago, studying electrodynamics in curved space-time I found1 that Maxwell s equations impose on space-time a restriction which can be formulated by saying that a certain vector q determined by the curvature field must be the gradient of a scalar function, or... 

The accurate quantum mechanical first-principles description of all interactions within a transition-metal cluster represented as a collection of electrons and atomic nuclei is a prerequisite for understanding and predicting such properties. The standard semi-classical theory of the quantum mechanics of electrons and atomic nuclei interacting via electromagnetic waves, i.e., described by Maxwell electrodynamics, turns out to be the theory sufficient to describe all such interactions (21). In semi-classical theory, the motion of the elementary particles of chemistry, i.e., of electrons and nuclei, is described quantum mechanically, while their electromagnetic interactions are described by classical electric and magnetic fields, E and B, often represented in terms of the non-redundant four components of the 4-potential, namely the scalar potential and the vector potential A. 

In field theory, electric charge [6] is a symmetry of action, because it is a conserved quantity. This requirement leads to the consideration of a complex scalar field . The simplest possibility [U(l)] is that have two components, but in general it may have more than two as in the internal space of 0(3) electrodynamics which consists of the complex basis ((1),(2),(3)). The first two indices denote complex conjugate pairs, and the third is real-valued. These indices superimposed on the 4-vector give a 12-vector. In U(l) theory, the indices (1) and (2) are superimposed on the 4-vector, 4M in free space, so, 4M in U(l) electrodynamics in free space is considered as transverse, that is, determined by (1) and (2) only. These considerations lead to the conclusion that charge is not a point localized on an electron rather, it is a symmetry of action dictated ultimately by the Noether theorem [6]. 

To consider magnetic flux density components of IAIV, Q must have the units of weber and R, the scalar curvature, must have units of inverse square meters. In the flat spacetime limit, R 0, so it is clear that the non-Abelian part of the field tensor, Eq. (6), vanishes in special relativity. The complete field tensor F vanishes [1] in flat spacetime because the curvature tensor vanishes. These considerations refute the Maxwell-Heaviside theory, which is developed in flat spacetime, and show that 0(3) electrodynamics is a theory of conformally curved spacetime. Most generally, the Sachs theory is a closed field theory that, in principle, unifies all four fields gravitational, electromagnetic, weak, and strong. 

E. Baum, Vector and Scalar Potentials away from Sources, and Gauge Invariance in Quantum Electrodynamics, Physics Note 3 (1991). 

In 1904 Whittaker [28] showed that any EM field or wave consists of two scalar potential functions, initiating what is known as superpotential theory [77]. By Whittaker s [8] 1903 paper, each of the scalar potential functions is derived from internally structured scalar potentials. Hence all EM fields, potentials, and waves may be expressed in terms of sets of more primary interior or infolded longitudinal EM waves and their impressed dynamics.35 This is indeed a far more fundamental electrodynamics than is presently utilized, and one that provides for a vast set of new phenomenology presently unknown to conventional theorists. 

Further, in 1904 Whittaker [56] (see also Section V.C.2) showed that any electromagnetic field, wave, etc. can be replaced by two scalar potential functions, thus initiating that branch of electrodynamics called superpotential theory [58]. Whittaker s two scalar potentials were then extended by electrodynamicists such as Bromwich [59], Debye [60], Nisbet [61], and McCrea [62] and shown to be part of vector superpotentials [58], and hence connected with A. 

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