  Well defined quantum field theory (QFT) for the electroweak force including
quantum electrodynamics (QED) and the weak force is obtained by considering
natural unitary representations of a group $K\subset U(2,2)$, where $K$ is
locally isomorphic to $SL(2,{\bf C})\times U(1)$, on a state space of Schwartz
spinors, a Fock space ${\mathcal F}$ of multiparticle states and a space
${\mathcal H}$ of fermionic multiparticle states which forms a Grassmann
algebra. These algebras are defined constructively and emerge from the
requirement of covariance associated with the geometry of space-time. (Here $K$
is the structure group of a certain principal bundle associated with a given
M\"{o}bius structure modeling space-time.) Scattering processes are associated
with intertwining operators between various algebras, which are encoded in an
associated bundle of kernel algebras. Supersymmetry emerges naturally from the
algebraic structure of the theory. Kernels can be generated using $K$ covariant
matrix valued measures given a suitable definition of covariance. It is shown
how Feynman propagators, fermion loops and the electron self energy can be
given well defined interpretations as measures covariant in this sense. An
example of the methods described in the paper is given in which the first order
Feynman amplitude of electro-electron scattering ($ee\rightarrow ee$) is
derived from a simple order (2,2) kernel. A second example is given explaining
muon decay which is a manifestation of the weak force.
