  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.
