Chiral Symmetry in Light-front QCD

The definition of chiral transformations in light-front field theory is very different from the conventional form in equal-time formalism. We study the consistency of chiral transformations and chiral symmetry in light-front QCD and derive a complete new light-front axial-vector current for QCD. The breaking of chiral symmetry in light-front QCD is only associated with helicity flip interaction between quarks and gluons. Remarkably, the new axial-vector current does not contain the pion pole part so that the associate chiral charge smoothly describes pion transitions for various hadronic processes.Comment: 15 pages, no figure, JHEP style, added reference and corrected typos and some changed conten

Does DLCQ S-matrix have a covariant continuum limit?

We develop a systematic DLCQ perturbation theory and show that DLCQ S-matrix does not have a covariant continuum limit for processes with $p^+=0$ exchange. This implies that the role of the zero mode is more subtle than ever considered in DLCQ and hence must be treated with great care also in non-perturbative approach. We also make a brief comment on DLCQ in string theory.Comment: 4 pages, 2 figure

Zero-mode contribution to the light-front Hamiltonian of Yukawa type models

Light-front Hamiltonian for Yukawa type models is determined without the framework of canonical light-front formalism. Special attention is given to the contribution of zero modes.Comment: 14 pages, Latex, revised version with minor changes, Submitted to J.Phys.

Variational Calculation of the Effective Action

An indication of spontaneous symmetry breaking is found in the two-dimensional $\lambda\phi^4$ model, where attention is paid to the functional form of an effective action. An effective energy, which is an effective action for a static field, is obtained as a functional of the classical field from the ground state of the hamiltonian $H[J]$ interacting with a constant external field. The energy and wavefunction of the ground state are calculated in terms of DLCQ (Discretized Light-Cone Quantization) under antiperiodic boundary conditions. A field configuration that is physically meaningful is found as a solution of the quantum mechanical Euler-Lagrange equation in the $J\to 0$ limit. It is shown that there exists a nonzero field configuration in the broken phase of $Z_2$ symmetry because of a boundary effect.Comment: 26 pages, REVTeX, 7 postscript figures, typos corrected and two references adde

Decoupling of Zero-Modes and Covariance in the Light-Front Formulation of Supersymmetric Theories

We show under suitable assumptions that zero-modes decouple from the dynamics of non-zero modes in the light-front formulation of some supersymmetric field theories. The implications for Lorentz invariance are discussed.Comment: 8 pages, revtex, 3 figure

Dynamical Chiral Symmetry Breaking on the Light Front.II. The Nambu--Jona-Lasinio Model

An investigation of dynamical chiral symmetry breaking on the light front is made in the Nambu--Jona-Lasinio model with one flavor and N colors. Analysis of the model suffers from extraordinary complexity due to the existence of a "fermionic constraint," i.e., a constraint equation for the bad spinor component. However, to solve this constraint is of special importance. In classical theory, we can exactly solve it and then explicitly check the property of ``light-front chiral transformation.'' In quantum theory, we introduce a bilocal formulation to solve the fermionic constraint by the 1/N expansion. Systematic 1/N expansion of the fermion bilocal operator is realized by the boson expansion method. The leading (bilocal) fermionic constraint becomes a gap equation for a chiral condensate and thus if we choose a nontrivial solution of the gap equation, we are in the broken phase. As a result of the nonzero chiral condensate, we find unusual chiral transformation of fields and nonvanishing of the light-front chiral charge. A leading order eigenvalue equation for a single bosonic state is equivalent to a leading order fermion-antifermion bound-state equation. We analytically solve it for scalar and pseudoscalar mesons and obtain their light-cone wavefunctions and masses. All of the results are entirely consistent with those of our previous analysis on the chiral Yukawa model.Comment: 23 pages, REVTEX, the version to be published in Phys.Rev.D; Some clarifications in discussion of the LC wavefunctions adde

NAMBU-GOLDSTONE BOSON ON THE LIGHT-FRONT

Spontaneous breakdown of the continuous symmetry is studied in the framework of discretized light-front quantization. We consider linear sigma model in 3+1 dimensions and show that the careful treatment of zero modes together with the regularization of the theory by introducing NG boson mass leads to the correct description of Nambu-Goldstone phase on the light-front.Comment: To appear in the proceedings of the 13th Symposium on Theoretical Physics, Mt. Sorak, Korea, from 27 June to 2 July, 1994