Automorphism groups of composition algebras and quark models

In this the authors study the automorphisms and derivations of real composition algebras with a view to its physical interpretations. They obtain canonical forms with a special stress in the four and eight dimensional cases. Also, using this description, they work with two mathematical models which describe some particles with certain observables in a surprising way. A first model, split g2, describes two observables for three quarks, their antiquarks, and eight mesons combining the quarks involved. A second one, so(4,4) circle-plus so(2,2), describes all the observables for all quarks (u, d, s, c, b and t)