Auxiliary field method in 4- and 3-dimensional Nambu–Jona-Lasinio models

Abstract

In order to check the validity of the auxiliary field method in the Nambu--Jona-Lasinio model, the one-loop (= quantum) effects of auxiliary fields on the gap equation are considered with N-component fermion models in four and three dimensions. N is not assumed very large but is 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 (\ensuremath{\chi}SB) is restored in $D=4$ and $D=3$ when the four-Fermi coupling is large. However, \ensuremath{\chi}SB is enhanced in a small coupling region in $D=3.$