QED Fermi-Fields as Operator Valued Distributions and Anomalies

Details QED Fermi-Fields as Operator Valued Distributions and Anomalies QED Fermi-Fields as Operator Valued Distributions and Anomalies

2004-09-24

arxiv.org/abs/math-ph/0409068v1

Few Body Syst. 36 (2005) 103-109

Physics

Mathematical Physics

soumis le 22/09/2004

Scientific paper

10.1007/s00601-004-0085-8

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.

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