FERMION DETERMINANTS AND EFFECTIVE ACTIONS

Configuration space heat-kernel methods are used to evaluate the deter minant and hence the effective action fur a SU(2) doublet of fermions in interaction with a covariantly constant SU(2) background field. Exa ct results are exhibited that are applicable to any Abelian background on which the only restriction is that (B-2-E(2)) and E . B are consta nt. Such fields include the uniform field and the plane wave field. Th e fermion propagator is also given in terms of gauge covariant objects . An extension to include finite temperature effects is given and the probability for creation of fermions from the vacuum at finite tempera ture in the presence of an electric field is discussed. (C) 1997 Ameri can Institute of Physics.