On the Physics of a Cool Pion Gas

At finite temperature, the Nambu-Goldstone bosons of a spontaneously broken chiral symmetry travel at a velocity $v < 1$. This effect first appears at order $\sim T^4$ in an expansion about low temperature, and can be related to the appearence of two distinct pion decay constants in a thermal bath. We discuss some consequences on the thermodynamics of a gas of massless pions.