General Parametrization Of Divergent Loop-diagrams And A Simple Strategy For Renormalization

As the essential program for dealing with ultraviolet divergences in quantum field theories, renormalization is indispensable in quantum electrodynamics (QED) that has been deemed as the most precise and successful field theory. It is also indispensable in the standard model of particle physics as successful quantum gauge theories. Furthermore, renormalization is also needed in the grand unified theories and the possible super-symmetric physics.However, conventional renormalization programs always necessitate specific regularization methods to isolate the divergences, which would inevitably destroy some symmetries of the original theories, or bring about some deformations that could not readily measured, some methods even are not consistent. As far as we know, no regularization is applicable in all kinds of field theories, each known regularization has certain shortcomings and fails somewhere. The real importance of a regularization method lies in the isolation of divergences in a manner that maintain the fundamental structures or symmetries of the original theory as far as possible, so a regularization method must avoid the introduction of violations of symmetries or deformations into the original theories, and it should also be simple, universal, and capable of practical calculations.In this paper, we introduce a simple strategy for renormalization basing on the effective field theory philosophy, which incorporate no artificial regularization or deformations, ambiguous local quantities would show up in place of divergences. The essential procedures of our strategy are:we start with a complete theory that is supposed to be underlying the quantum field theory in consideration, then we perform differentiation and integration with respect to external momenta on the ill-defined or UV divergent Feynman integrals to evaluate the divergent Feynman amplitudes. The results of such treatments would be definite non-local quantities plus local ambiguities. The ambiguities could be further reduced through imposing gauge and/or other symmetries, with the remaining ones to be fixed through confronting with physical boundary conditions.We demonstrated our new strategy with QED at one-loop level. As was shown in our deductions, provided QED is taken as an effective theory, finite results could be readily obtained after exploiting Lorentz and gauge invariances and imposing a few elementary boundary conditions, no specific regularization is introduced here. In the meantime, it is easy to see that the conventional programs could be viewed as subtle means for obtaining such results. In addition, we also calculated the two-point vertex functions of the Wess-Zumino model as the simplest super-symmetric field theory at one-loop level, with which we discussed the reduction of the ambiguities due to super-symmetric Ward identities and Lorentz invariance. Through concrete computation, we showed that super-symmetry could be consistently imposed or preserved at least at one-loop level without using any specific regularization. This is a virtue of our approach that absent in the conventional programs:they are either in conflict with super-symmetry (e.g., the popular't Hooft-Veltman scheme of dimensional regularization) or not consistent (e.g., the dimensional reduction).