Dimensional regularization vs methods in fi xed dimension with and without y5

Abstract

We study the Lorentz and Dirac algebra, including the antisymmetric e tensor and the y 5 matrix, in implicit gauge-invariant regularization/renormalization methods de ned in xed integer dimensions. They include constrained differential, implicit and four-dimensional renormalization. We nd that these xed-dimension methods face the same di culties as the different versions of dimensional regularization. We propose a consistent procedure in these methods, similar to the consistent version of regularization by dimensional reduction.