Dynamical Chiral Symmetry Breaking on the Light Front I. DLCQ Approach
arXiv:hep-th/9907071 · doi:10.1103/PhysRevD.61.045009
Abstract
Dynamical chiral symmetry breaking in the DLCQ 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 bare mass is absent. A quantum analysis demonstrates that a nonperturbative mean-field solution to the ``zero-mode constraint'' for a scalar boson (sigma) can develop a nonzero condensate 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 fermionic field, which resolves a seemingly inconsistency between triviality of the null-plane chiral charge Q_5|0>=0 and nonzero condensate. We also calculate masses of scalar and pseudoscalar bosons for both symmetric and broken phases, and eventually derive the PCAC relation and nonconservation of Q_5 in the broken phase.
Revised version to appear in Phys. Rev. D. 19 pages, 4 figures, REVTEX. Derivation of the PCAC relation is given. Its relation to the nonconservation of chiral charge is clarified. 1 figure and some references added
References in corpus (5)
- Quantum Chromodynamics and Other Field Theories on the Light Cone
- NJL model on the light cone and pion structure function
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Cited by in corpus (10)
- Heavy Quarkonium in a Holographic Basis
- Space-like and time-like pion electromagnetic form factor and Fock state components within the Light-Front dynamics
- Statistical Physics and Light-Front Quantization
- Dynamical Chiral Symmetry Breaking on the Light Front.II. The Nambu--Jona-Lasinio Model
- Fermionic Zero Modes and Spontaneous Symmetry Breaking on the Light Front
- Chiral Symmetry in Light-front QCD
- Chiral Condensates in the Light-Cone Vacuum
- Light Mesons on the Light Front
- Light-Cone Quantization: Foundations and Applications
- Vector Mesons on the Light Front