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It is shown that, at finite temperature, chiral invariance does not imply that fermion propagators have poles at K^2=0. Instead, a zero-momentum fermion has energy K^0=M, where M^2=g^{2C (R) T^2}8 and C (R) is the quadratic Casimir of the fermion representation. The dispersion relation for K0 is computed and can be crudely approximated (to within 10%) by K^0 ({M^2+{K}^2) }^1{2}. Applications to high-temperature QCD, SU (2) (1), and grand unified theories are discussed.
H. Arthur Weldon (Mon,) studied this question.