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.

We present a discussion where the choice of the regularization procedure and the routing for the internal lines momenta are put at the same level of arbitrariness in the analysis of Ward identities involving simple and well-known problems in quantum field theory. They are the complex self-interacting scalar field and two simple models where the scalar-vector-vector and axial-vector-vector process are pertinent. We show that, in all these problems, the conditions to symmetry relations preservation are put in terms of the same combination of divergent Feynman integrals, which are evaluated in the context of a very general calculational strategy, concerning the manipulations and calculations involving divergences. Within the adopted strategy, all the arbitrariness intrinsic to the problem are still maintained in the final results and, consequently, a perfect map can be obtained with the corresponding results of traditional regularization techniques. We show that, when we require an universal interpretation for the arbitrariness involved, in order to get consistency with all stated physical constraints, a strong condition is imposed for regularizations which automatically eliminates the ambiguities associated to the routing of the internal lines momenta of loops. The conclusion is clean and sound: the association between ambiguities and unavoidable symmetry violations in Ward identities cannot be maintained if an unique prescription is required for identical situations in the evaluation of divergent physical amplitudes.

We show that ambiguities and symmetry violations arising in one loop calculations can always be avoided provided the regularization scheme employed satisfies three consistency conditions. Our calculations are effected by assuming only implicitly the presence of a regulator in the integrand. We demonstrate in this way that there is a set of three relations involving divergent integrals of the same degree of divergence which are the source of both ambiguities and symmetry violations in Quantum Electrodynamics. Moreover we give analytical expressions for the finite parts of amplitudes off the mass shell systematized in terms of a set of special functions. Ward identities require hightly nom trivial relations involving those functions which we also derive.

We analyse a new strategy to manipulate and calculate divergent amplitudes in the context of Quantum Electrodynamics. We compare our results with results of Dimensional Regularization and (one parameter) Pauli-Villars regularization prescriptions and conclude that the present technique allows for an unambiguous determination of the physical content of the divergent amplitude. The results obtained for QED can be easily extended to nonrenormalizable theories where they should be most especially useful.