Chiral Symmetry {\it Breaking} in the Light-Cone Representation ($M_\pi^2 \sim \mu_q <\Omega |\bar{\psi}\psi|\Omega > +...$)

TL;DR

This paper explores how vacuum structure and condensates manifest in the light-cone representation, focusing on the linear dependence of pion mass squared on fermion bare mass, with detailed analysis in two dimensions and speculative discussion in four dimensions.

Contribution

It provides a detailed examination of chiral symmetry breaking and vacuum structure in the light-cone framework, highlighting the mechanism behind pion mass dependence.

Findings

Vacuum structure and condensates are analyzed in light-cone representation.

Pion mass squared depends linearly on fermion bare mass.

Detailed two-dimensional analysis with speculative four-dimensional discussion.

Abstract

In this paper I shall discuss the way in which vacuum structure and condensates occur in the light-cone representation. I shall particularly emphasize the mechanism by which the mass squared of a composite such as the pion comes to depend linearly on the bare mass of its Fermion constituents. I shall give details in two dimensions then discuss the case of four dimensions more speculatively.