Auxiliary Field Method in 4- and 3- dimensional Nambu--Jona-Lasinio Models

Abstract

In order to check the validity of auxiliary field method in the Nambu--Jona-Lasinio model, the one-loop (=quantum) effects of auxiliary fields to the gap equation are considered with N-component fermion models in 4 and 3 dimensions. N is not assumed so large but regarded as a loop expansion parameter. To overcome infrared divergences caused by the Nambu-Goldstone bosons, an intrinsic fermion mass is assumed. It is shown that the loop expansion can be justified by this intrinsic mass whose lower limit is also given. It is found that due to quantum effects, chiral symmetry breaking ($\chi$SB) is restored in D=4 and D=3 when the four-Fermi coupling is large. However, $\chi$SB is enhanced in a small coupling region in D=3.

16 pages, 12 figures

References in corpus (12)

• Dynamical Flavor Symmetry Breaking by a Magnetic Field in $2+1$ Dimensions
• Universality and the magnetic catalysis of chiral symmetry breaking
• Nambu-Jona-Lasinio Model in Curved Space-Time
• Meson loops in the Nambu-Jona-Lasinio model
• Nonlinear sigma model approach for chiral fluctuations and symmetry breakdown in Nambu-Jona-Lasinio model
• Two Phase Transitions in Chiral Gross-Neveu Model in $2+\epsilon$ Dimensions at Low N
• No Spontaneous Breakdown of Chiral Symmetry in Nambu-Jona-Lasinio Model
• Nambu-Jona-Lasinio Model in Curved Spacetime with Magnetic Field
• The Auxiliary Field Method as a Powerful Tool for Nonperturbative Study
• Effect of Dynamical SU(2) Gluons to the Gap Equation of Nambu--Jona-Lasinio Model in Constant Background Magnetic Field
• Nambu-Jona-Lasinio Model Coupled to Constant Electromagnetic Fields in D-Dimension
• Higher Dimension Operators and Chiral Symmetry Breaking in Nambu-Jona-Lasinio Model

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• Vector-type four-quark interaction and its impact on QCD phase structure
• Path Integral Bosonization of the 't Hooft Determinant: Quasiclassical Corrections
• Anatomy of the dense QCD matter from canonical sectors
• Next to leading order calculation with dimensional regularization in Nambu--Jona-Lasinio Model
• The Auxiliary Field Method in Quantum Mechanical Four-Fermi Models -- A Study Toward Chiral Condensation in QED