Ward-Takahashi identities at finite temperature and phase structure in (2+1)-dimensional chiral Gross-Neveu model.

Abstract

Chiral Ward-Takahashi identities with composite fields are generalized to finite temperature and applied to investigate the chiral phase transition and phase structure in the (2+1)-dimensional chiral Gross-Neveu model. In terms of these identities, the mass spectra of fermions and bound states and the Goldberger-Treiman relation at finite temperature are obtained. The vertex correction between the fermion and bound states [sigma] is evaluated beyond the leading order in the 1/[ital N] expansion at zero and finite temperatures. With the aid of the gap equation derived from Ward-Takahashi identities, the phase structure is discussed at zero and finite temperatures. It turns out that (i) at zero temperature, the vertex correction is very small and its influence on the phase structure can be neglected and (ii) at nonzero temperature, the infrared divergence in the vertex correction will make the results of the chiral phase transition obtained at the leading order invalid in next to the leading order and the phase structure is in agreement with Coleman's theorem.