The one-loop neutrino contribution to the gravitation propagator

Abstract

The one-loop neutrino correction to the gravitation propagator is calculated using the technique of dimensional regularization. The resulting amplitude satisfies Slavnov-Ward identities and the divergent part can be cancelled by a pole term of the form Δ L= √−g (2−ω)(4π) 2120 [R 2−3R μνR μν] . If, however, we are to avoid the appearance of a somewhat unusual anomaly it is essential that the counterterm be in a continuous (2ω) number of dimensions rather than 4, in which case Δ L= √−g2 ω (2−ω)(4π) 232(4ω 2−1) [ 1 2 ω′R 2−(2ω−1)R μνR μν0] .