ONE-LOOP THERMAL FIELD-THEORY IN 3 DIMENSIONS

We consider thermal field theory in three dimensions to one-loop order using the quantum-mechanical path integral. Upon reexpressing the sum over winding numbers by the Poisson resummation formula, and then usi ng an integral representation for the sum, we find that the temperatur e dependence of the generating functional can be expressed in closed f orm at one-loop order. In a pure scalar theory, only Green's functions with two external vertices have temperature dependence, while, in a g auge theory, one has temperature dependence only if there are two, thr ee, or four external spatial vectors in the static limit. The eta func tion that occurs when one considers a quantum spinor field in a backgr ound gauge field vanishes for all temperatures larger than zero.