A Model of Composite Electrons and Photons

Abstract

It is shown that electrons and photons can be considered as composities of particles representating the fundamental representation of the extended Lorentz group $SU(3)\otimes SU(3)$ in (8+1) dimensional space-time which are held together by force mediated by gauge particles belonging to the regular representation. In this theory, spin states of electron, positron and photon belong to the $8\otimes 8$ representation of the group. The fine structure constant of the fundamental gauge interaction is found to be unity from the fact that the photon is massless. The mass of the fundamental particles constituting the electron and the photon is estimated to be $\geq 10^{21}$ GeV from the experimental limit for the life-time of electron decay into neutrino and photon which is a consequence of the model. This corresponds to distances of less than $10^{-35}$ cm which is smaller than the Planck length indicating thereby that the composite nature of electrons and photons will be revealed when we go to Planckian energies.