Spontaneous symmetry breaking in discretized light-cone field theory

The problem of spontaneous symmetry breaking in scalar field theories quantized on the light cone is considered. Within the framework of "discretized" light-cone field theory, a constrained zero mode of the scalar field, which is necessary for obtaining a consistent dynamics, is responsible for supporting nonzero vacuum expectation values classically. This basic structure is shown to carry over to the quantum theory as well, and the consistency of the formalism is checked in an explicit perturbative calculation in (1+1)-dimensional ${\phi }^4$ theory.