INFRARED REGULARIZATION IN QUANTUM-GRAVITY

Infrared regularization of Feynman amplitudes in perturbative quantum gravity is discussed. Two familiar strategies, momentum cutoff and mas sification, are critically reviewed. Both methods rely on cancellation s (in cross sections) between infrared divergences in individual Feynm an diagrams on the one hand, and the contributions of soft gravitons o il the other. Cutoffs at the low end of momentum integration have been widely accepted in the context of quantum gravity, though long abando ned in QED; this method is highly ambiguous. The paper is therefore mo stly concerned with the alternative strategy of introducing a regulati ng graviton mass. Difficulties of several kinds arise. Conflicts with the experimental tests of general relativity have been known for a lon g lime, but this is not an absolute deterrent since the experimental u ncertainties are considerable. More serious are internal inconsistenci es that are reponed here, Me believe, for the first time. We insist th at the massified theory must be internally consistent and iind that th is 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); t he massless limit necessarily involves five degrees of freedom and mas sless 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 p rinciple, and this in rum suggests that the theory is inconsistent in the next higher order. There are strong indications that additional fi elds are needed, most likely an antisymmetric tensor field that could be identified with the antisymmetric part of the vierbein. (C) 1996 Ac ademic Press, Inc.