Schwinger and seagull terms in spinor electrodynamics and the dimensional regularization method

Abstract

It is found that the extension of a local theory of fields, specifically quantum electrodynamics, to a space of continuous dimensionality together with a systematic interpretation of the relativistically invariant functions as distributions, gives rise to a rather formal but operative machinery which naturally leads to the existence of non-vanishing c-number Schwinger and seagull terms. In fact, with this kind of tool at hand, no ad hoc definitions are required to deal with products of field operators taken at the same space-time point. We present a complete analysis of the behavior of Schwinger and seagull terms as analytic functions of the number of dimensions of the space ( v). It is also shown that the Feynman conjecture (cancellation of Schwinger terms with divergences of seagulls) holds for arbitrary v.