Broken Chiral Symmetry on a Null Plane

TL;DR

This paper explores how spontaneous chiral symmetry breaking is represented on a null-plane in QCD, showing that all effects are contained in Hamiltonians and deriving related formulas, with implications for understanding QCD condensates.

Contribution

It provides a general proof of Goldstone's theorem on a null-plane and establishes a mapping between chiral-symmetry breaking condensates and null-plane condensates.

Findings

Null-plane Hamiltonians contain all effects of chiral symmetry breaking.

Derived the null-plane Gell-Mann-Oakes-Renner formula.

Showed the operator algebra reduces to SU(2N) symmetry in a certain limit.

Abstract

On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincar\'e generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone's theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann-Oakes-Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model.