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

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

2003-06-02

arxiv.org/abs/hep-th/0306008v1

Phys.Rev. D68 (2003) 065002

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 12 figures

Scientific paper

10.1103/PhysRevD.68.065002

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.

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