Effective action at finite temperature

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Abstract
We consider the problem of generalizing the usual effective potential calculations by computing the kinetic terms in the one-loop effective action. Results for the leading-order gradient terms in the effective action for scalar fields valid for both zero and finite temperatures are given when quantum corrections arise from scalar, spinor, or gauge fields. In the gauge field calculation we present a generalization of the 't Hooft gauge-fixing condition which removes cross terms in the scalar and gauge fields, resulting in considerable simplification of the fluctuation operators. Our results imply that the consistency of the one-loop effective action requires at least three families of fermions.