Vector fields 0 electrodynamics

In this final section, it is shown that the three magnetic field components of electromagnetic radiation in 0(3) electrodynamics are Beltrami vector fields, illustrating the fact that conventional Maxwell-Heaviside electrodynamics are incomplete. Therefore Beltrami electrodynamics can be regarded as foundational, structuring the vacuum fields of nature, and extending the point of view of Heaviside, who reduced the original Maxwell equations to their presently accepted textbook form. In this section, transverse plane waves are shown to be solenoidal, complex lamellar, and Beltrami, and to obey the Beltrami equation, of which B is an identically nonzero solution. In the Beltrami electrodynamics, therefore, the existence of the transverse 1 = implies that of , as in 0(3) electrodynamics. 

A three-way cross-check of the self-consistency of the 0(3) ansatz can be carried out starting from Eq. (459), in which A is complex because the electromagnetic field in 0(3) electrodynamics carries a topological charge k/,4i0 . The vector field A in the internal space of 0(3) symmetry must depend on by special relativity and can be written as... 

BELTRAMI VECTOR FIELDS IN ELECTRODYNAMICS—A REASON FOR REEXAMINING THE STRUCTURAL FOUNDATIONS OF CLASSICAL FIELD PHYSICS ... 

When we come to examine the annals of classical hydrodynamics and electrodynamics, we find that the foundations of vector field theory have provided some key field structures whose role has repeatedly been acknowledged as instrumental in not only underpinning the structural edifice of classical continuum field physics, but in accounting for its empirical exhibits as well. 

When we consider time-harmonic electrodynamics in more general media (chiral-biisotropic), A. Lakhtakia also underscored the importance of the Beltrami field condition [54], In particular, he found that time-harmonic EM fields in a homogeneous reciprocal biisotropic medium are circularly polarized, and must be described by Beltrami vector fields. 

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