The Standard Model Architecture and Interactions
© 2011 Claude Michael Cassano
Based on my 1984 linearization of the Klein-Gordon equations, potential functions generalizations of the electric and magnetic field strengths form a basis from which a compound model simply constructs the leptons; the simple differences between the quarks and leptons; how the quarks arose from the leptons; why there are these two types of fermions; and why there are precisely three generations for each of these types. The most elementary particle interactions classify the interactions between strong and weak, and further still between the W and Z type of weak interactions. Two simple conservation requirements give rise to all the fundamental particle interactions, and describe the structure of the weak intermediate envelopes. Further, a simple charge function determines the charge of every object. Further still, the only free assignable parameters for the entire model are four mass constants for each fermion generation.
This presentation is essentially a summary of my book: "a Mathematical Preon Foundation for the Standard Model"; but starting from the different standpoint of my Helmholtzian operator matrix product, rather than my constructive algebras (developed primarily in "Reality is a Mathematical Model" and "The Weighted Matrix Product").
Through some ingenious mathematical manipulations, it can be shown that in free space, the thus defined E and B (generalizations of the electric and magnetic field strengths) also satisfy the Klein-Gordon equations, so have a particle-nature.
Identifying a particle-nature member R as either an E or a B ; each of these members satisfies the Klein-Gordon equation, but only really do so as three-vectors with three components or triplets. And, each bag of triplets must be triplets or triplets of triplets or triplets of triplets of triplets, and so on (i.e.: 3 to the n of triplets).
The simplest , and thus, most fundamental members are triplets. The next most fundamental is triplets of triplets.
These will be considered, here.
Denoting a triplet of triplets by: S sub R ≡ (R sub1,R sub2,R sub3)
is a 3 matrix.
Then we can write:
S sub E ≡ (E sub1,E sub2,E sub3) , and S sub B ≡ (B sub1,B sub2,B sub3).
The leptons and all the colors and flavors of quarks correspond to these
L's , Λ's , and Q's ; by the associations given, here.
The table shown, may be considered a replica of the one found everywhere, including Wikipedia (except that the quark colors are explicitly delineated).
Shown, are examples of hadrons (second order compositions): mesons: and baryons.
The charge function acts as a linear function on any linear combination of S sub R matrix objects, independant of column/generation,.
The function for mass is a little more complicated, but for the first and second order objects is shown, here.
As mentioned earlier, this has been a summary of my book, "a Mathematical Preon Foundation for the Standard Model", available on Kindle through amazon.com. Find links to all my books at: