Dimensional regularization in four dimensions

Abstract

A new gauge invariant ultraviolet regularization proposed recently is discussed for Abelian gauge theories. This cut-off scheme resembles closely the canonical dimensional regularization (CDR), but it is formulated strictly in four dimensions. In a sense, it may be conceived as a continuous superposition of Pauli-Villars cut-offs. Although it differs from the CDR for a general graph, for some closed fermion loops the two schemes coincide. The new cut-off procedure is also well-suited for practical calculations of Feynman diagrams in the α-parametric representation; in this respect it preserves the merits of CDR. Such a “dimensional regularization in four dimensions” obviously does not suffer from the conceptual problems connected with the definition of theγ5 matrix, which plague conventional DR schemes. Nevertheless, some spurious anomalies in the closed fermion loops do occur, similarly to the Pauli-Villars scheme.