QED Fermi Fields as Operator-Valued Distributions and Anomalies

Abstract.

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 the use of test functions which are a 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 QED₂ is exemplified in a simple way.