Propagation of Cool Pions

Abstract

For an exact chiral symmetry which is spontaneously broken at zero temperature, we show that at nonzero temperature, generally pions travel at {\it less} than the speed of light. This effect first appears at next to leading order in an expansion about low temperature. When the chiral symmetry is approximate we obtain two formulas, like that of Gell-Mann, Oakes, and Renner, for the static and dynamic pion masses.