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

Abstract

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, that is fully responsible for ensuring the Ward and Ward-Takahashi identities are satisfied, and a transverse part. The transverse part is decomposed into 8 independent components each being separately free of kinematic singularities in $\mathbf{any}$ covariant gauge in a basis that modifies that proposed by Ball and Chiu. Analytic expressions for all 11 components of the $O(\alpha )$ vertex are given explicitly in terms of elementary functions and one Spence function. These results greatly simplify in particular kinematic regimes.

Comments: 35 pages, latex, 2 figures, Complete postscript file available from: ftp://cpt1.dur.ac.uk/pub/preprints/dtp95/dtp9506/dtp9406.ps