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The Dirac Equation is a Special Case of the Maxwell-Cassano Equations/nFor vector Phi of D The Klein-Gordon equation may be written (see reference (4)):/nWhenever Phi of D is a 2 to the M-dimensional vector, via a matrix differential operator factorization, it may be written (in the Dirac representation), as shown here: and, since these matrix operators are commutative: conformability of the matrices requires thatthese matrices are all 2×1 matrices; yielding: /nFor symmetry purposes, let: t=ix^0 then, combining into a single matrix equation,/n Just as there are a number of representations of the Dirac equation, there is more than one matrix operator factorization of the Maxwell-Cassano equations (3). A matrix operator factorization of the Maxwell-Cassano equations may be compactly written, from references (1) and (3) as follows: For the stationary state the source/sink density term vanishes in the Maxwell-Cassano equations, which allows an equating of the Maxwell-Cassano equation & Dirac equation factorizations. These may imply correlations between the Dirac equation and the Maxwell-Cassano equations as the correspondences/mappings: m⇔|m| and -θ_sub_D_to_the_j = f_to_the_h./nThe Dirac equation may be expanded with the above notation as shown/nAs reference (1) shows. the component pairs may be organized such that this organization exhibits the mass-generalization of Maxwell's equations, but organizing them while comparing them analogously to the Dirac equations yields the shown/nAnd, Continuing the comparison with the Maxwell-Cassano equations in the special case: m_sub_zero = -m , m_sub_1=m_sub_2=m_sub_3 = 0:/nSo, extending the Dirac equation beyond the source/sink free case (so looking beyond just eigenvalues and eigenvectors); and writing in matrix form, and comparing: Then, viewing each matrix as a paired sum: In this form the transformations are easy to see: By the invertible matrix theorem each matrix is invertible. Thus, these transformations are oneto - bijective. From the first matrices on each side of the sum, the rest of the transformations are even more easily seen. The full set of transformations are shown, here/nThis proves that the mass-generalized Maxwell's equations (Maxwell-Cassano equations) is a more general analysis of fundamental-elementary particle phenomena. It further proves that the Lagrangian is far simpler than that consisting of the Glashow-Salam-Weinberg + fermion + Higgs + Yukawa kludge. Also, it explains the group structure and architecture of the fermions, as shown in reference (2). It also proves that those with wealth to seek the truth choose not to do so, but with all deceivableness and unrighteousness in them they have not the love of the truth, but rather embrace strong delusion, that they profess a lie. References and further readings (1) Cassano, Claude.Michael ; "Reality is a Mathematical Model", 2010. ISBN: 1468120921 ; http://www.amazon.com/dp/1468120921 ASIN: B0049P1P4C ; http://www.amazon.com/Reality-Mathematical-Modelebook/ dp/B0049P1P4C/ref=tmm(kin(swatch(0?(encoding=UTF8&sr=&qid= (2) Cassano, Claude.Michael ; "A Mathematical Preon Foundation for the Standard Model", 2011. ISBN:1468117734 ; http://www.amazon.com/dp/1468117734 ASIN: B004IZLHI2 ; http://www.amazon.com/ Mathematical-Preon-Foundation-Standardebook/dp/B004IZLHI2/ref=tmm(kin(swatch(0?(encoding=UTF8&sr=&qid= Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 1" ; http://www.dnatube.com/video/6907/ The-Standard-Model-Architecture-and-Interactions-Part-1 http://www.scivee.tv/node/28362 Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 2" ; http://www.youtube.com/watch?v=Mxa2u7-czmk Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 2" ; http://www.dnatube.com/video/6908/ The-Standard-Model-Architecture-and-Interactions-Part-2/n(3) Cassano, Claude.Michael ; "A Helmholtzian operator and electromagnetic-nuclear field" ; http://www.dnatube.com/video/6877/ A-Helmholtzian-operator-and-electromagnetic-nuclear-field http://www.scivee.tv/node/27991/n(4) Cassano, Claude.Michael ; "A Brief Mathematical Look at the Dirac Equation" ; https://independent.academia.edu/CLAUDEMICHAELCASSANO read/download pdf at: http://viXra.org/abs/1504.0006

Channels: Physics (General) Particle physics Mathematics

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