Cutoff Regularization Method in Gauge Theories

A Lorentz and gauge symmetry preserving regularization method is discussed in four dimension based on momentum cutoff. We use the conditions of gauge invariance or equivalently the freedom of shift of the loop momentum to define the evaluation of the terms carrying even number of Lorentz indices, e.g. proportional to $k_{\mu}k_{\nu}$. The remaining scalar integrals are calculated with a four dimensional momentum cutoff. The finite terms (independent of the cutoff) are free of ambiguities coming from subtractions in non-trivial cases. Finite parts of the result are equal with the results of dimensional regularization. The proposed method can be applied to various physical processes where the use of dimensional regularization is subtle or a physical cutoff is present. As a famous example it is shown that the triangle anomaly can be calculated unambiguously with this new improved cutoff.