Topology 0 electrodynamics

Several of Tesla s patented circuits exhibit this effect, as analyzed and rigorously shown by Barrett [41]. However, this can only be seen when the circuits are examined in a higher-topology electrodynamics. Barrett s analysis is in quaternionic electrodynamics. Tensor analysis will not show it. 

The basic theories of physics - classical mechanics and electromagnetism, relativity theory, quantum mechanics, statistical mechanics, quantum electrodynamics - support the theoretical apparatus which is used in molecular sciences. Quantum mechanics plays a particular role in theoretical chemistry, providing the basis for the valence theories which allow to interpret the structure of molecules and for the spectroscopic models employed in the determination of structural information from spectral patterns. Indeed, Quantum Chemistry often appears synonymous with Theoretical Chemistry it will, therefore, constitute a major part of this book series. However, the scope of the series will also include other areas of theoretical chemistry, such as mathematical chemistry (which involves the use of algebra and topology in the analysis of molecular structures and reactions) molecular mechanics, molecular dynamics and chemical thermodynamics, which play an important role in rationalizing the geometric and electronic structures of molecular assemblies and polymers, clusters and crystals surface, interface, solvent and solid-state effects excited-state dynamics, reactive collisions, and chemical reactions. 

I. Topological Basis for Higher-Symmetry Electrodynamics II. Basis in Fiber Bundle 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. 

The development just given illustrates the fact that the topology of the vacuum determines the nature of the gauge transformation, field tensor, and field equations, as inferred in Section (I). The covariant derivative plays a central role in each case for example, the homogeneous field equation of 0(3) electrodynamics is a Jacobi identity made up of covariant derivatives in an internal 0(3) symmetry gauge group. The equivalent of the Jacobi identity in general relativity is the Bianchi identity. 

In this section, the field equations (31) and (32) are considered in free space and reduced to a form suitable for computation to give the most general solutions for the vector potentials in the vacuum in 0(3) electrodynamics. This procedure shows that Eqs. (86) and (87) are true in general, and are not just particular solutions. On the 0(3) level, therefore, there exist no topological monopoles or magnetic charges. This is consistent with empirical data—no magnetic monopoles of any kind have been observed in nature. 

Therefore, the vacuum charge and current densities of Panofsky and Phillips [86], or of Lehnert and Roy [10], are given a topological meaning in 0(3) electrodynamics. In this condensed notation, the vacuum 0(3) field tensor is given by... 

THE LINK BETWEEN THE TOPOLOGICAL THEORY OF RANADA AND TRUEBA, THE SACHS THEORY, AND 0(3) ELECTRODYNAMICS... 

The topological approach of Ranada and Trueba, the general relativistic approach of Sachs, and the 0(3) electrodynamics are interlinked and shown to be based on the concept of Faraday s lines of force. 

The Aharonov-Bohm effect requires topological consideration [1], (i.e., a structured vacuum), and there exist conservation laws of topological origin, the simplest one is given by the sine-Gordon equation, which also appears in the discussion of 0(3) electrodynamics by Evans and Crowell [5]. 

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... 

Therefore, the B(3) held can be dehned in terms of lines of force, and the topological considerations of Ranada and Trueba [1] can be extended to 0(3) electrodynamics, and thence to the Sachs theory. 

In this short review, we have extended the topological considerations of Ranada and Trueba [1] to 0(3) electrodynamics [3] and therefore also linked these concepts to the Sachs theory reviewed elsewhere in this three-volume compilation [2]. In the same way that topology and knot theory applied to the Maxwell-Heaviside theory produce a rich structure, so does topology applied to the higher-symmetry forms of electrodynamics such as the Sachs theory and 0(3) electrodynamics. 

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