A gauge covariant approximation to QED

We examine the fermion propagator in quenched QED in three and four dimension using gauge covariant approximation which preserves Ward-Takahashi Identity with appropriate renormalization to smooth the threshold behaviour of the fermion self energy .Thus we avoid the infrared singurality in three dimension. The behaviour of the fermion propagator in three dimension near the threshold is then found to be similar to the one in four dimension instead gauge technique provides gauge invariant behaviour .We esitimate the solutions for a pair of spectral functions in the Landau gauge in three dimension by using inequalities .We find analytic solutions for arbitrary gauges in four dimension . The full propagators are expressed in terms of hypergeometric function in four dimension . The vacuum expectation value is shown to be finite after reguralization of ultraviolet divergence both in three and four dimension and vanishes in the weak coupling limit in three dimension .