Fermion Determinants and Effective Actions

Configuration space heat-kernel methods are used to evaluate the determinant and hence the effective action for an SU(2) doublet of fermions in interaction with a {\it covariantly constant} SU(2) background field. Exact results are exhibited which are applicable to {\it any} Abelian background on which the only restriction is that $(B^{2}-E^{2})$ and $E\cdot B$ are constant. Such fields include the uniform field and the plane wave field. The 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 temperature in the presence of an electric field is discussed.