From Dimensional to Cut-Off Regularization

We extent the standard approach of dimensional regularization of Feynman diagrams: we replace the transition to lower dimensions by a 'natural' cut-off regulator. Introducing an external regulator of mass Lambda^(2e), we regain in the limit e -> 0 and e > 0 the results of dimensional and cut-off regularization, respectively. We demonstrate the versatility and adequacy of the different regularization schemes for practical examples (such as non covariant regularization, the axial anomaly or regularization in effective field theories).