Effective fermion masses of order $gT$ in high-temperature gauge theories with exact chiral invariance

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} = \frac{g^{2} C (R) T^{2}}{8}

and

C (R)

is the quadratic Casimir of the fermion representation. The dispersion relation for

\vec{K} \neq 0

is computed and can be crudely approximated (to within 10%) by

K^{0} \approx {(M^{2} + {\vec{K}}^{2})}^{\frac{1}{2}}

. Applications to high-temperature QCD, SU(2)×U(1), and grand unified theories are discussed.

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Effective fermion masses of ordergTin high-temperature gauge theories with exact chiral invariance