Sommaire:

The dimensional quantum electrodynamics with massless fermions is studied in a covariant gauge. The main new ingredient is an operator solution of the Dirac equation expressed directly in terms of fields present in the original Lagrangian. This permits us analyze in detail residual gauge symmetry present in the covariant gauge. For the sake of a comparison, we study first an analogous solution in a non-gauge Thirring-Wess model and its implications for the axial anomaly arising from the necessity to correctly define products of fermion operators via point splitting. In the Schwinger model, one has to define currents in a gauge invariant way. Certain problems with the usual definition of the vector and axial-vector currents are identified that obscure the origin of massive gauge boson (Schwinger mechanism). We reformulate the model in a finite volume, defining the currents correctly, and clarify the role of the gauge zero mode in the axial anomaly and in the Schwinger mechanism.

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