Ghost couplings in causal quantum gravity

Abstract

In a recent paper we studied gauge invariance of perturbative quantum gravity in the causal Epstein - Glaser approach. The present work continues this study by examining the most general form of the ghost coupling which, together with the graviton self-interaction (derived from the Einstein - Hilbert Lagrangian), gives a coupling that is gauge invariant to first order. It turns out that this ghost coupling depends on 27 free parameters and can be written as the sum of the ghost coupling derived from a proposal by Kugo and Ojima and a general divergence and a coboundary. Because gauge invariance to first order does not imply gauge invariance at second order, we then discuss several couplings found in the literature up to second-order tree graphs and present a particularly simple one, which consists of only two ghost vertices and is gauge invariant at first and second order. This coupling is very convenient for the investigation of radiative corrections. The present work is focused on tree graphs, since they are the most subtle point in the study of gauge invariance in the causal approach.