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Lack of strong ellipticity in Euclidean quantum gravity

Ivan G Avramidi-+ and Giampiero Esposito++

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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.


PACS

04.60.-m Quantum gravity

02.40.Dr Euclidean and projective geometries

02.40.Vh Global analysis and analysis on manifolds

MSC

58J32 Boundary value problems on manifolds

35Jxx Partial differential equations of elliptic type (See also 58J10, 58J20)

83C45 Quantization of the gravitational field

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 5 (May 1998)

Received 1 September 1997, in final form 12 February 1998



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