Low energy theorems in a nonlocal chiral quark model at finite temperature

We solve the Dyson equation and the Bethe-Salpeter equation for a nonlocal effective quark interaction kernel which is instantaneous and separable. The momentum-dependent dynamical quark mass, the scalar and pseudoscalar meson masses, the pion decay constant and the quark meson coupling constant are calculated at finite temperature in the Hartree approximation for the quark self energy. We obtain relations between these quantities, which coincide to leading order in the current quark mass (m ₀/Δm) with the basic low energy theorems: the Goldstone theorem, the Gell-Mann-Oakes-Renner relation and the Goldberger-Treimann relation at finite temperature. A formula for the σ?π mass gap is obtained which exhibits an additional contribution from the momentum dependence of the quark mass.