Lack of strong ellipticity in Euclidean quantum gravity

Details Lack of strong ellipticity in Euclidean quantum gravity Lack of strong ellipticity in Euclidean quantum gravity

1997-08-29

arxiv.org/abs/hep-th/9708163v1

Class.Quant.Grav. 15 (1998) 1141-1152

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, Plain Tex, 33 KB, no figures

Scientific paper

10.1088/0264-9381/15/5/006

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.

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