  The solution of the O$(N) \phi^4$ scalar field theory in the broken phase is
given in the framework of light cone quantization and a 1/N expansion. It
involves the successive building of operator solutions to the equation of
motion and constraints including operator zero modes of the fields which are
the LC counterpart to the equal time non trivial vacuum effects. The
renormalization of the procedure is accomplished up to $2^{nd}$ order in the
1/N expansion for the equation of motion and constraints. In addition the
renormalization of the divergent contributions of the 2-point and 4-point
functions is performed in a covariant way. The presence of a zero modes leads
to genuine non perturbative renormalization features.
