New Kernels in Quantum Gravity

Details New Kernels in Quantum Gravity New Kernels in Quantum Gravity

1999-06-22

arxiv.org/abs/hep-th/9906169v2

Class.Quant.Grav. 16 (1999) 3999-4010

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, plain Tex. In this revised version, section 5 is new, section 3 is longer, and the presentation has been improved

Scientific paper

10.1088/0264-9381/16/12/317

Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary operator for mixed boundary conditions of local nature a two-by-two matrix of pseudo-differential operators with pseudo-homogeneous kernels. The request of invariance of such boundary conditions under infinitesimal gauge transformations leads to non-local boundary conditions on ghost fields. In Euclidean quantum gravity, an alternative scheme is proposed, where non-local boundary conditions and the request of their complete gauge invariance are sufficient to lead to gauge-field and ghost operators of pseudo-differential nature. The resulting boundary conditions have a Dirichlet and a pseudo-differential sector, and are pure Dirichlet for the ghost. This approach is eventually extended to Euclidean Maxwell theory.

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