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

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

2007-08-23

arxiv.org/abs/0708.3176v2

Phys.Rev.D77:025008,2008

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.77.025008

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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