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 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.

13 pages, 11 figures; v2: typos corrected (Eqs. 4 and 44)

References in corpus (1)

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

Cited by in corpus (6)

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• Derivative corrections to the Heisenberg-Euler effective action
• Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model
• Untwisting twisted NJL${}_2$-kinks by a bare fermion mass
• Exploring new states of matter with a photonic emulator
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation