Light-front realization of chiral symmetry breaking (Q2774335)

The authors discuss various aspects of the light-front (LF) formulation of relativistic quantum physics, and certain advantages it has over the conventional, equal-time (ET) formalism. The perspective taken is that of `vacuum physics', that is, the study of properties of zero-modes of respective models. The LF vacuum in particular has distinctive properties of simplicity: Provided the LF energy \(p^-\) is positive semidefinite, then also the longitudinal momentum \(p^+\) is \(\geq 0\) and thus the LF Fock vacuum decouples from nonzero momentum states, which cannot be combined to obtain zero momentum. This property, amongst others, simplifies the description of excited states and might relate to the constiuent quark model of quantum chromodynamics. Such a constituent model should emerge as a result of dynamical chiral symmetry breaking (D\(\chi\)SB), and thus a nontrivial, chirally broken ET vacuum, which coexists with the trivial LF vacuum. NEWLINENEWLINENEWLINEThis raises the three fundamental questions the authors answer in detail by considering a number of physically relevant models: NEWLINENEWLINENEWLINEi) What is the difference between the ordinary chiral transformation and that on the LF? NEWLINENEWLINENEWLINEA most remarkable point is that the massive fermion is chirally invariant, a property which yet seems to be exceptional in view of the other models considered. As far as regards symmetry breaking, it is usually identified by nonzero vacuum expectation values of order parameters, in a nontrivial vacuum state different from the Fock vacuum. However the LF vacuum is kinematically determined to be the Fock vacuum, the information about symmetry breaking must be encoded in the dynamics. NEWLINENEWLINENEWLINEii) How does the gap equation for the chiral condensate emerge? NEWLINENEWLINENEWLINEThe dynamical information alluded to can be expected to be contained in constraint equations for the `bad component' of the field in a chiral basis, which is always a constrained variable in the LF formalism. It is shown how such a constraint turns into a gap equation for the minimum energy of the chiral condensate in three models: The sigma model of scalar fields, the chiral Yukawa model, and the Nambu-Jona-Lasino (NJL) model of purely fermionic fields. The approach used is the discretized light-cone quantization method. NEWLINENEWLINENEWLINEiii) What is the consequence of the coexistence of the trivial LF Fock vacuum and the nonzero chiral condensate? NEWLINENEWLINENEWLINEOne of the peculiarities here is the loss of mass information, due to the fact that the Fock vacuum does not distinguish between different Fermion masses, which is only encoded dynamically in the Hamiltonians. The emerging picture is that chiral symmetry breaking on the LF is characterized by multiple Hamiltonians rather than multiple vacua. This entails yet some more interesting consequences: The Nambu-Goldstone bosons are easily described by few constituent fields, as is shown explicitly in the NJL model. Furthermore the LF chiral charge is not conserved in the broken phase, due to properties of the pertinent Hamiltonian. NEWLINENEWLINENEWLINEThe authors add some thoughts about the possible coupling of gauge fields, which leads, however, to a rather complicated zero-mode structure. Nevertheless, the zero mode remains important for the description of D\(\chi\)SB as is shown in the case of the Abelian Higgs model. NEWLINENEWLINENEWLINEApart from its original contributions to current research, the article provides a largely self-contained, pedagocically structured, and modern overview of the LF formalism.