ONE-LOOP QED VERTEX IN ANY COVARIANT GAUGE - ITS COMPLETE ANALYTIC FORM

The one-loop vertex in QED is calculated in arbitrary covariant gauges as an analytic function of its momenta. The vertex is decomposed into a longitudinal part, which is fully responsible for ensuring that the Ward and Ward-Takahashi identities are satisfied, and a transverse pa rt. The transverse part is decomposed into eight independent component s each being separately free of kinematic singularities in any covaria nt gauge in a basis that modifies that proposed by Ball and Chiu. Anal ytic expressions for all 11 components of the O(alpha) vertex are give n explicitly in terms of elementary functions and one Spence function. These results greatly simplify in particular kinematic regimes.