Boundary Operators in Euclidean Quantum Gravity

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  • 5 March 1996
Abstract
Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that, on choosing the de Donder functional, the resulting boundary operator involves projection operators jointly with a nilpotent operator. Hence the elliptic operator acting on metric perturbations is not symmetric. Other choices of mixed boundary conditions, for which the normal components of metric perturbations can be set to zero at the boundary, are then analyzed in detail. This leads to the evaluation of the 1-loop divergency in the axial gauge for gravity. Interestingly, such a divergency turns out to coincide with the one resulting from transverse-traceless perturbations.

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