  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.
