MIXED BOUNDARY-CONDITIONS IN EUCLIDEAN QUANTUM-GRAVITY

This paper studies a new set of mixed boundary conditions in Euclidean quantum gravity. These involve, in particular, Robin boundary conditi ons on the perturbed 3-metric and hence lead, by gauge invariance, to Robin conditions on the whole ghost 1-form. The corresponding trace an omaly is evaluated in the case of a Bat Euclidean 4-space bounded by a 3-sphere. In general, this anomaly differs from the ones resulting fr om other local or non-local boundary conditions studied in recent lite rature.