QED Fermi-Fields as Operator Valued Distributions and Anomalies

Pierre Ca Grange (1) , Ernst Werner (2)

1 PMT - Laboratoire de Physique Mathématique et Théorique
2 ITP - Institut fur Theoretische Physik

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.

Mots clés: QED; Distributions; Causality; Anomalies

Domaines: Physique mathématique [math-ph]

Pierre Ca Grange, Ernst Werner. QED Fermi-Fields as Operator Valued Distributions and Anomalies. Light Cone 2004, 2004, Amsterdam, Netherlands. ⟨hal-00002930v2⟩