Chiral Symmetry and Vertex Symmetry in the Extended Moeller-Rosenfeld Model

TL;DR

This paper explores how vertex symmetry in interacting fermions leads to an $SU(2N)_W$ invariant Lagrangian, connecting chiral symmetry and vertex symmetry through a principle of maximum smoothness of quark wave functions.

Contribution

It demonstrates that vertex symmetry induces an $SU(2N)_W$ invariance and derives approximate $SU(6)_W$ and chiral symmetries from a maximum smoothness principle.

Findings

Vertex symmetry results in an $SU(2N)_W$ invariant Lagrangian.

Approximate $SU(6)_W$ and chiral symmetries are derived from wave function smoothness.

The principle of maximum smoothness links symmetries in the extended Moeller-Rosenfeld model.

Abstract

Vertex symmetry for interacting fermions will be shown to lead to a Lagrangian exhibiting $SU(2N)_W$ invariance associated with the subgroup $SU(2N)_q \times SU(2N)_{\bar{q}}$ generated by $C$-odd and $C$-even spin operators. Approximate $SU(6)_W$ vertex symmetry as well as chiral invariance will then be shown to follow from a principle of maximum smoothness (M\"oller-Rosenfeld) of the bound state quark wave function.