Propagation of cool pions

For an exact chiral symmetry that is spontaneously broken at zero temperature, we show that, at nonzero temperature, generally pions travel at less than the speed of light. This effect first appears at next-to-leading order in an expansion around 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. copyright 1996 The American Physical Society