Spontaneous Symmetry Breaking in Discretized Light-Cone Quantization

Spontaneous symmetry breaking of the light-front Gross-Neveu model is studiedin the framework of the discretized light-cone quantization. Introducing ascalar auxiliary field and adding its kinetic term, we obtain a constraint onthe longitudinal zero mode of the scalar field. This zero-mode constraint issolved by using the $1/N$ expansion. In the leading order, we find a nontrivialsolution which gives the fermion nonzero mass and thus breaks the discretesymmetry of the model. It is essential for obtaining the nontrivial solution totreat adequately an infrared divergence which appears in the continuum limit.We also discuss the constituent picture of the model. The Fock vacuum istrivial and an eigenstate of the light-cone Hamiltonian. In the large $N$limit, the Hamiltonian consists of the kinetic term of the fermion with dressedmass and the interaction term of these fermions.Comment: 25 pages, Latex, no figures, to be published in Progress of Theoretical Physic