Generally -- if the amending groupings that work to form the homology of a given arbitrary superstring of discrete energy permittivity, are here to be of the nature of being abelian groupings -- then, the directly corresponding discrete quantum of energy is then said to have an abelian light-cone-gauge topology. (Kaluza-Klein). Such correlative discrete quanta of energy, tend to bear a relatively supplemental oriented set of second-order light-cone-gauge eigenstates. Furthermore -- it is generally the case, that, if the amending groupings that work to form the homology of a given arbitrary superstring of discrete energy permittivity, are here to be of the nature of being non abelian groupings -- then, the directly corresponding discrete quantum of energy is then said to have a non abelian light-cone-gauge topology. (Yang-Mills). Such correlative discrete quanta of energy, tend to bear a relatively sinusoidal oriented set of second-order light-cone-gauge eigenstates.
There are two exceptions that I can think of "from the top of my head" -- non-scattered electromagnetic energy and tachyons. Electromagnetic energy has a homology-related structure, that is comprised of by abelian groupings (it is of a cohomological nature, as it is of a symplectic geometry.) Yet, since non-scattered discrete quanta of electromagnetic energy have second-order light-cone-gauge eigenstates, that are here to have of a relatively sinusoidal nature, -- non-scattered electromagnetic energy is of a Yang-Mills nature. (Non-Scatteted electromagnetic energy works to bear a non abelian light-cone-gauge topology.)
Whereas, -- tachyons work to bear second-order light-cone-gauge eigenstates that are relatively supplemenatal. Yet, since its homology-related structure is comprised of by non abelian groupings -- tachyons are of a Yang-Mills nature. (Tachyons work to bear a non abelian light-cone-gauge topology.)
I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach
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