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

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 nonlinear Dirac equation. Its solution reproduces the full semiclassical results including the Dirac sea to any desired accuracy. Dynamical effects from the Dirac sea are encoded in higher order derivative terms and multifermion interactions with perturbatively calculable, finite coefficients. Characteristic differences between models with discrete and continuous chiral symmetry are observed and clarified.