The Equations of the Electron

Here, my preon foundation of the standard model architecture of the electron is analyzed in light of the mass-generalized Maxwell's equations which illuminates this foundation. The simplest elementary particles in the preon model of the standard model are the first order objects (including electrons and their neutrinos). Recall that a first order object may be described by (R,R,R) (where R represents either a E or a B component). The d'Alembertian factorization is a compact expression of Maxwell's equations. The Helmholtzian factorization generalization of the d'Alembertian factorization is a compact expression of the mass-generalized Maxwell's equations. Up to now I haven't considered how the preon architecture the mass-generalized Maxwell's equations manifests themselves satisfy the mass-generalized Maxwell's equations. Each first and second order object is a combination of E&B components, and it is not altogether obvious that these combinations would satisfy them. So, what follows is an examination of these objects on this matter, and what a fundamental object must satisfy if it is to have such an architecture and satisfy the mass-generalized Maxwell's equations. Of course, vanishing of all the field potentials A_{σ}^{i} for a given σ will satisfy these, but a more general solution may be obtained (including this) by analyzing all these equations,. A soliton 'stationary' traveling wave solution to the Klein Gordon equation, is presented, here. For the non-vacuum scheme of each fermion, given it's architecture; the mass-generalized Maxwell's equations may be used to write it's densities in terms of these potentials. Now, every fundamental object satisfies the mass-generalized Maxwell's equations (Maxwell-Cassano equations). For each particle, it's architecture shapes the field. The instance of the electron (a B scenario architecture) , is developed in detail, here. From these and the above, information on the densities from the potentials may be obtained (or vice-versa). No mathematical inconsistencies have arisen by this architecture for the electron. Visit my author page on amazon.com to find my books available on Kindle in digital and some in print at the website shown here: http://www.amazon.com/-/e/B008MD6CVS and Visit the link, here: http://www.barnesandnoble.com/s/claude-michael-cassano?store=allproducts&keyword=claude+michael+cassano for my books available on NOOK and some in print at Barnes & Noble.

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