Zero mode of the Gross-Neveu model in discretized light-cone field theory

We study the spontaneous chiral symmetry breaking in discretized light-cone field theory using the Gross-Neveu model. With the help of the 1N expansion, zero mode of the field operator is obtained nonperturbatively by solving the constraint relation involving the zero mode. The zero mode has c-number part at the lowest order, by which the discrete chiral symmetry is broken. Renormalization is done by use of the constraint relation of the zero mode, and we get explicitly the operator part of the zero mode which is O(1N).