Spontaneous Breakdown of U(1) symmetry in DLCQ without Zero Mode

We show that the spontaneous breakdown of U(1) symmetry in a Higgs model can be described in discretized light cone formulation even by neglecting zero mode. We obtain correctly the energy of a ground state with the symmetry breakdown. We also show explicitly the presence of a Goldstone mode and its absence when the U(1) symmetry is gauged. In spite of obtaining the favorable results, we lose a merit in the formulation without zero modes that a naive Fock vacuum is the true ground state.