Light-front realization of chiral symmetry breaking

We discuss a description of chiral symmetry breaking in the light-front (LF ) formalism. Based on careful analyses of several models, we give clear ans wers to the following three fundamental questions: (i) What is the differen ce between the LF chiral transformation and the ordinary chiral transformat ion? (ii) How does a gap equation for the chiral condensate emerge? (iii) W hat is the consequence of the coexistence of a nonzero chiral condensate an d the trivial Fock vacuum? The answer to Question (i) is given through a cl assical analysis of each model. Question (ii) is answered based on our reco gnition of the importance of characteristic constraints, such as the zero-m ode and fermionic constraints. Question (iii) is intimately related to anot her important problem, reconciliation of the nonzero chiral condensate [<(< psi>)over cap>psi] not equal 0 and the invariance of the vacuum under the L F chiral transformation Q(5)(LF) \9] = 0. This and Question (iii) are under stood 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 Q(5)(LF) is no longer conserved and th at the transformation of the scalar and pseudoscalar fields is modified. We also discuss other outcomes, such as the light-cone wave function of the p seudoscalar meson in the Nambu-Jona-Lasinio model.