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Dynamical chiral symmetry breaking in the discretized light-cone quantization method is investigated in detail using a chiral Yukawa model closely related to the Nambu-Jona-Lasinio model. By classically solving three constraints characteristic of the light-front formalism, we show that the chiral transformation defined on the light front is equivalent to the usual one when the bare mass is absent. A quantum analysis demonstrates that a nonperturbative mean-field solution to the ''zero-mode constraint'' for a scalar boson can develop a nonzero condensate ͗͘ϭϪ(/N)͗⌿ ⌿͘ 0 while a perturbative solution cannot. This description is due to our identification of the ''zero-mode constraint'' with the gap equation. The mean-field calculation clarifies unusual chiral transformation properties of the fermionic field, which resolves a seeming inconsistency between the triviality of the null-plane chiral charge Q 5 LF ͉0͘ϭ0 and the nonzero condensate ͗⌿ ⌿͘ 0. We also calculate masses of scalar and pseudoscalar bosons for both symmetric and broken phases, and eventually derive the relation of partial conservation of axial vector current and nonconservation of Q 5 LF in the broken phase.

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

We discuss a description of chiral symmetry breaking in the light-front (LF) formalism. Based on careful analyses of several models, we give clear answers to the following three fundamental questions: (i) What is the difference between the LF chiral transformation and the ordinary chiral transformation? (ii) How does a gap equation for the chiral condensate emerge? (iii) What is the consequence of the coexistence of a nonzero chiral condensate and the trivial Fock vacuum? The answer to Question (i) is given through a classical analysis of each model. Question (ii) is answered based on our recognition of the importance of characteristic constraints, such as the zero-mode and fermionic constraints. Question (iii) is intimately related to another important problem, reconciliation of the nonzero chiral condensate and the invariance of the vacuum under the LF chiral transformation. This and Question (iii) are understood in terms of the modified chiral transformation laws of the dependent variables. The characteristic ways in which the chiral symmetry breaking is realized are that the chiral charge is no longer conserved and that the transformation of the scalar and pseudoscalar fields is modified. We also discuss other outcomes, such as the light-cone wave function of the pseudoscalar meson in the Nambu-Jona-Lasinio model.Comment: 26 pages, no figure, REVTEX, Journal versio