Goldstone's Theorem on a Light-Like Plane

TL;DR

This paper reviews chiral symmetry and Goldstone's theorem on null planes, showing how chiral constraints lead to a spin-flavor algebra in QCD with massless flavors, connecting null-plane and traditional approaches.

Contribution

It demonstrates how chiral symmetry constraints on null-plane Hamiltonians can be solved to recover the SU(2N) spin-flavor algebra in QCD, linking different theoretical frameworks.

Findings

Chiral symmetry constraints can be explicitly solved on null planes.

The SU(2N) spin-flavor algebra emerges from these constraints.

The approach connects null-plane formalism with Weinberg's results.

Abstract

I review various aspects of chiral symmetry and its spontaneous breaking on null planes, including the interesting manner in which Goldstone's theorem is realized and the constraints that chiral symmetry imposes on the null-plane Hamiltonians. Specializing to QCD with N massless flavors, I show that there is an interesting limit in which the chiral constraints on the null-plane Hamiltonians can be solved to give the spin-flavor algebra SU(2N), recovering a result originally found by Weinberg using different methods.