  The treatment of fields as operator valued distributions (OPVD) is recalled
with the emphasis on the importance of causality following the work of Epstein
and Glaser. Gauge invariant theories demand the extension of the usual
translation operation on OPVD, thereby leading to a generalized $QED$
formulation. At D=2 the solvability of the Schwinger model is totally
preserved. At D=4 the paracompactness property of the Euclidean manifold
permits using test functions which are decomposition of unity and thereby
provides a natural justification and extension of the non perturbative heat
kernel method (Fujikawa) for abelian anomalies. On the Minkowski manifold the
specific role of causality in the restauration of gauge invariance (and mass
generation for $QED_{2}$) is examplified in a simple way.
