Regularizations: a unique prescription for all situations

Abstract

A detailed investigation on the possible role played by the intrinsic arbitrariness of the perturbative evaluation of physical amplitudes and their symmetry relations, initiated in a first work, is continued. Previously announced results are detailed presented. The very general calculational method, concerning the divergences manipulations and calculations, adopted to discuss the questions of ambiguities and symmetry relations, in purely fermionic divergent Green functions, is applied to explicit evaluate three-point functions. Two of such functions, the well known Scalar-Vector-Vector and Axial-Vector-Vector triangle amplitudes are considered in details. Given the fact that within the adopted strategy, all the arbitrariness intrinsic to the problem are maintained in the final results, and that it is possible to map them in to the ones of traditional techniques, clean and sound conclusions can be extracted. In particular, we can map our results in to the Dimensional Regularization ones as well as in to those corresponding to surface's terms evaluation. The first above cited amplitude can be treated within the Dimensional Regularization while the second do not and, consequently, it is usually treated by the surface's terms evaluation strategy. Within the adopted strategy both problems can be equally treated. We show that when we require consistency in the interpretations of the intrinsic indefinitions present in the perturbative amplitudes, which means to treat all physical amplitudes on the same way, no room is left for the ambiguities. As a natural consequence, the physical amplitudes are obtained symmetry preserving, where they must be, and anomalous, where they need to in spite of being non-ambiguous.

Proof of Renormalizability of Scalar Field Theories Using the Epstein-Glaser Scheme and Techniques of Microlocal Analysis

“…The regularization essentially separates divergent integrals into finite and infinite parts, these last ones are ultimately absorbed in the redefinition of parameters with renormalization. Although, many regularization methods have been quite successful, there are ambiguities associated to the extracting of the finite part of a divergent integral [22,23,24], which is natural since even the more fundamental axioms of arithmetic are only applied to numbers. However, since every physical process in perturbative quantum field theory (PQFT) is expressed in terms of Feynman propagators, which are not functions but The first step towards a more rigorous treatment of PQFT is due to H. Epstein and V. J. Glaser [3].…”