Integrating out the Dirac sea: Effective field theory approach to exactly solvable four-fermion models

TL;DR

This paper develops an effective field theory for positive energy fermions in 1+1 dimensional Gross-Neveu models, accurately reproducing semi-classical results and clarifying differences between models with discrete and continuous chiral symmetry.

Contribution

It derives microscopically effective Lagrangians that incorporate Dirac sea effects for exactly solvable four-fermion models, advancing understanding of baryon dynamics.

Findings

Effective Lagrangians reproduce semi-classical results with high accuracy

Higher order derivatives and multi-fermion interactions encode Dirac sea effects

Differences between discrete and continuous chiral symmetry models are clarified

Abstract

We use 1+1 dimensional large N Gross-Neveu models as a laboratory to derive microscopically effective Lagrangians for positive energy fermions only. When applied to baryons, the Euler-Lagrange equation for these effective theories assumes the form of a non-linear Dirac equation. Its solution reproduces the full semi-classical results including the Dirac sea to any desired accuracy. Dynamical effects from the Dirac sea are encoded in higher order derivative terms and multi-fermion interactions with perturbatively calculable, finite coefficients. Characteristic differences between models with discrete and continuous chiral symmetry are observed and clarified.