A Soliton Solution to the Klein-Gordon Equation/n My preon foundation for the fermions and mass-generalized Maxwell's equations hint at and are consistent with this soliton solution. Mass is not generally considered as a four-vector, but considering it as such is consistent with the mass-generalized Maxwell's equations and this solution. That mass is not generally considered a 4-vector is because only it's magnitude is manifested in the Klein-Gordon equation and the resulting non-relativistic Schroedinger equation, Newton's laws, etc. But the generalization of Maxwell's equations to include mass at the very ;east suggests it. The analysis here shows the relationship and how the fermion architecture is manifested by the 4-vector mass, And The analysis, here shows that considering mass as a four vector allows a general solution of the Klein-Gordon equation. Now, since x⁰ = ct , m⋅r is of the form k⋅r-ωt (for 3-space r ). And, thus, such a potential is represented as a traveling wave soliton solution of the Klein-Gordon equation. (Note that zero-densities dual potentials ( σ & σ ) may exist as such in the vacuum.) And so, we see that /nke^{-|m⋅r|} /nis a soliton solution of the Klein-Gordon equation, /nThe following related graphs are also worth noting. /nVisit my author page on amazon.com to find my books available on Kindle in digital and some in print at the website shown here:/nhttp://www.amazon.com/-/e/B008MD6CVS/nand Visit the link, here: /nhttp://www.barnesandnoble.com/s/claude-michael-cassano?store=allproducts&keyword=claude+michael+cassano/nfor my books available on NOOK and some in print at Barnes & Noble.

Channels: Physics (General) Particle physics

Tags: soliton Klein-Gordon Maxwell's equations physics fermion physics preon

Uploaded by: cloudmichael ( Send Message ) on 15-11-2013.

Duration: 0m 0s