Pion dispersion relation at finite temperature in the linear sigma model from chiral Ward identities

We develop one-loop effective vertices and propagators in the linear sigma model at finite temperature satisfying the chiral Ward identities. We use t hese in rum to compute the pion dispersion relation in a pion medium for sm all momentum and temperatures on the order of the pion mass at next to lead ing order in the parameter m(pi)(2)/4 pi(2)f(pi)(2) and to zeroth order in the parameter (m(pi)/m(sigma))(2). We show that this expansion reproduces t he result obtained from chiral perturbation theory at leading order. The ma in effect is a perturbative, temperature-dependent increase of the pion mas s. We find no qualitative changes in the pion dispersion curve with respect to the leading order behaviour in this kinematical regime. (C) 2000 Elsevi er Science B.V. All rights reserved.