The toroid antenna as a conditioner of electromagnetic fields into (low energy) gauge fields

Treatment of the radiated ®eld from a toroid antenna as two A ®elds in resonance or a U ®eld, and the toroid as a U ®eld radiator, results in the prediction of (i) omnidirectional radiation patterns (with small indentations at the poles), and (ii) periodic resonances in the driving conditions. These predictions have been con®rmed experimentally, giving validity to the fundamental nature of this topological and group theory understanding of the ®rst order determinants of electromagnetic ®eld dynamics. Resonant gauge (U) ®elds are produced by a toroid radiator as either propagating or standing waves. In the case of a torus with a single winding, an alternating current driver will produce a series of nonmeasurable A vector potential resonances, which overlap and combine into measurable phase factor or gauge ®eld, U, waves. Such U waves, although generated on a toroidalsolenoidal structure of nonsimple topology, are yet spherical waves ± either standing spherical waves, or propagating spherical waves. The topological constraints of electromagnetic ®elds mapped to a torus driven by single or double wiring are described. It is shown that such mapping results in group symmetries higher than U (1), e.g., SU (2), and that electromagnetic activity is a€ected by such mapping, being determined by the symmetry forms. Underpinning these symmetry forms are topological conservation laws. The toroid antenna exhibits a series of low and high impedances and permits a U (1) to SU (2) mapping of e.m. ®elds over a ®ber bundle, as well as a mapping of rational and real numbers to complex numbers (in S for the nonresonant condition) and quaternions (in S for the resonant condition). When in resonance, the singly-wound and the doubly-wound (caduceous) torus emits radiation in SU (2)/Z2 form. The ®elds emitted for the resonantly driven toroid are alternatively self-dual and anti-self-dual (i.e., instanton solutions to the Maxwell equations of S). In resonance, the singly wound and the doubly wound torus produce ®elds which are both multiply connected, and of SU (2)/Z2 form (homeomorphic to S), as well as simply connected, and of SU (2) from (homeomorphic to S). This study has implications far beyond the immediate subject. If the conventional theory of electromagnetism, i.e., `Maxwell's theory', which is of U (1) symmetry form, is but the simplest local theory of electromagnetism, then those pursuing a uni®ed ®eld theory may wish to consider as a candidate ®eld for uni®cation not only this simple local theory, but other forms of `conditioned' electromagnetism. As is shown here, other such forms can be either force ®elds or gauge ®elds of higher group symmetry, e.g., SU(2) and above.