Quaternionic chromodynamics as a theory of composite quarks and leptons

I make a preliminary study of quaternionic chromodynamics [i.e., U(2) algebraic chromodynamics] as a theory of composite quarks and leptons. In the unphysical symmetric static limit in which the gluon field is massless and the fundamental two-internal-component spinor is infinitely massive, I compute the internal-symmetry structure of the residual interactions of three-spinor composites, using the heuristic quark and lepton identifications proposed by Harari and Shupe. Three types of interactions appear: (i) a color-singlet, flavor-diagonal photon, coupling to the electron, quarks, and neutrino with the correct charge assignments, and a second photon coupling to the neutrino and quarks, but not to the electron; (ii) color-changing, flavor-diagonal gluons, coupling to the quarks in a pattern resembling, but not identical to, SU(3) quantum chromodynamics; (iii) color-changing, flavor-changing gluons, three exchanges of which can produce a weak flavor-changing transition between color-singlet states, without requiring the existence of conventional intermediate bosons. While certain aspects of the symmetric static limit are clearly at variance with standard phenomenology, the results make it plausible that a more realistic calculation, taking symmetry breaking into account, may reproduce the observed features of the usual S${\mathrm{U}\left(3\right)\mathrm{}}_{\mathrm{color}}$ × ${\mathrm{}\left[\mathrm{S}\mathrm{U}\right(2\mathrm{})\times \mathrm{U}(1\left)\right]}_{\mathrm{w}\mathrm{e}\mathrm{a}\mathrm{k}-\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}}$ model. I briefly discuss some ideas about symmetry breaking, and describe a mechanism leading to topologically inequivalent quark-lepton generations.