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

Understand

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.