Symmetry preserving regularization with a cutoff

Abstract

Abstract:A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimensions based on a momentum cutoff. We use the conditions of gauge invariance or equivalently the freedom to shift the loop momentum to define the evaluation of the terms carrying even number of Lorentz indices, e.g. proportional to µ ν . 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 to that of dimensional regularization.

Corrections to gauge theories in effective quantum gravity with a cutoff

“…In case of divergent integrals it differs from (1), for non-divergent cases both substitutions give the same results at O(1/Λ 2 ) (the difference is a vanishing surface term). It is shown in [21] that this definition is robust in gauge theories, differently organized calculations of the 1-loop functions agree with each other using (2) and disagree using (1). For four free indices the gauge invariance dictates (n = 2, 3, ...)…”

“…A novel regularization of gauge theories is proposed in [21] based on 4 dimensional momentum cutoff to evaluate 1-loop divergent integrals. The idea was to construct a cutoff regularization which does not brake gauge symmetries and the necessary shift of the loop-momentum is allowed as no surface terms are generated.…”

“…Based on the diagrammatical proof of gauge invariance it can be shown that the two conditions are related and both are in connection with the requirement of vanishing surface terms. It was proposed in [21] that instead of (1) the general identification of the cutoff regulated integrals in gauge theories…”

“…Some methods can separate the divergences of the theories and does not rely on a physical cutoff [25,26,27] or even could be independent of it [28]. For further literature see references in [21].…”

“…Naively quadratic divergences are set to zero in the process, but already Veltman noticed that these divergences can be identified by calculating the poles in d = 2. Careful calculation of the Veltman-Passarino 1-loop functions in dimensional regularization and with 4-momentum cutoff leads to the following identifications [21,31,32] …”