Lack of strong ellipticity in Euclidean quantum gravity

Abstract

Recent work in Euclidean quantum gravity has studied boundary conditions which are completely invariant under infinitesimal diffeomorphisms on metric perturbations. On using the de Donder gauge-averaging functional, this scheme leads to both normal and tangential derivatives in the boundary conditions. In the present paper, it is proved that the corresponding boundary value problem fails to be strongly elliptic. The result raises deep interpretative issues for Euclidean quantum gravity on manifolds with boundary.

14 pages, Plain Tex, 33 KB, no figures

References in corpus (2)

• Heat-Kernel Asymptotics with Generalized Boundary Conditions
• Heat-kernel coefficients for oblique boundary conditions

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