THE NONLOCAL ODD-PARITY O(E(2)) EFFECTIVE ACTION OF QED(3) AT FINITE-TEMPERATURE

We study the odd-parity part of the one-loop gauge field self-energy i n QED(3) with massive fermions at finite temperature, with particular emphasis on the non-analyticity at zero momentum of the relevant scala r amplitude F-beta(p), which renders the O(e(2)) action intrinsically non-local. We analyse F-beta(p) in Minkowski space (real-time formalis m) both by dispersion relations and by direct evaluation. F-beta(p) is also studied in Euclidean space (imaginary-time formalism). In partic ular, we show explicitly how to analytically continue the Feynman-para metrized amplitude to Minkowski space, avoiding spurious singularities . We obtain the limiting behaviour of F-beta(p) along the lines p(0) = alpha \p\ for \p\ much less than \M\ (where M is the fermion mass) in both Euclidean and Minkowski space, and we show that the results are fully consistent. Useful approximate closed-form expressions are given for this low-p behaviour, which are shown numerically to be valid for energies and momenta up to the order of the fermion mass scale. The p ossibility that the action might be approximately local for some appro priate regime of parameters is explored using a simple non-static exte rnal gauge field configuration. (C) 1995 Academic Press, Inc.