Divergence of the axial current and fermion density in Gross-Neveu models

TL;DR

This paper investigates the divergence of the axial current in 1+1 dimensional Gross-Neveu models, relating fermion density derivatives to condensates and fermion mass, providing new insights into baryon number assignment.

Contribution

It introduces a novel use of axial current divergence to analyze fermion densities and resolves a conflict in baryon number assignment in these models.

Findings

Relates fermion density derivatives to condensates and mass

Clarifies baryon number assignment in multi-fermion states

Provides a new test of known results in Gross-Neveu models

Abstract

The divergence of the axial current is used to relate the spatial derivative of the fermion density to the bare fermion mass and scalar/pseudoscalar condensates in 1+1 dimensional Gross-Neveu models. This serves as a novel test of known results, to explain simple features of the continuous chiral model and to resolve a conflict concerning the assignment of baryon number to certain multi-fermion bound states.