Infrared Regularization in Quantum Gravity

Abstract

Infrared regularization of Feynman amplitudes in perturbative quantum gravity is discussed. Two familiar strategies, momentum cutoff and massification, are critically reviewed. Both methods rely on cancellations (in cross sections) between infrared divergences in individual Feynman diagrams on the one hand, and the contributions of soft gravitons on the other. Cutoffs at the low end of momentum integration have been widely accepted in the context of quantum gravity, though long abandoned in QED; this method is highly ambiguous. The paper is therefore mostly concerned with the alternative strategy of introducing a regulating graviton mass. Difficulties of several kinds arise. Conflicts with the experimental tests of general relativity have been known for a long time, but this is not an absolute deterrent since the experimental uncertainties are considerable. More serious are internal inconsistencies that are reported here, we believe, for the first time. We insist that the massified theory must be internally consistent and find that this modest requirement leads to conflict with the equivalence principle. Earlier work has shown that all mass singularities can be eliminated from the free theory by a change of variables (in the mass theory); the massless limit necessarily involves five degrees of freedom and massless linearized gravity is accompanied by a vector field and a scalar field, so that it has five degrees of freedom. The calculations have been completed to first order in the Newtonian coupling constant only, but this is enough to get us into a difficulty with the equivalence principle, and this in turn suggests that the theory is inconsistent in the next higher order. There are strong indications that additional fields are needed, most likely an antisymmetric tensor field that could be identified with the antisymmetric part of the vierbein.