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arXiv · 0708.3176

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

Felix Karbstein·Michael Thies
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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.

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Felix Karbstein, Michael Thies. 2007-11-29. Integrating out the Dirac sea: Effective field theory approach to exactly solvable four-fermion models. https://doi.org/10.1103/physrevd.77.025008

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