From arbitrariness to anomalies in two-dimensional perturbative calculations

A very general calculational strategy is applied to the evaluation of divergent physical amplitudes which are typical of 2D perturbative calculations. With this approach, in the final results all the arbitrariness intrinsic to the calculations, due to the divergent character, is still present. We show that, concerning the arbitrariness, the regularizations can be classified into two basic classes. The consequences on adopting each such class for the symmetry relations are investigated. It is noted that if very general symmetry requirements, such as Furry's theorem or gauge invariance, are used to select a consistent regularization procedure, the possible sources of ambiguities related to the choices for the internal line momenta of loops are completely eliminated. A very transparent description of the two-dimensional anomalies emerges, allowing a clear understanding of the results obtained within the context of traditional methods. The comparison with 4D triangle anomalies reveals a completely similar situation for both cases. The very interesting phenomenon of mass generation for the gauge boson in the massless fermion theory is also obtained in agreement with the expected results