Boundary operators in Euclidean quantum gravity
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. Moreover, the elliptic operator acting on metric perturbations is 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 analysed in detail. Lastly, the evaluation of the 1-loop divergence in the axial gauge for gravity is obtained. Interestingly, such a divergence turns out to coincide with the one resulting from transverse-traceless perturbations.
- Publication:
-
Classical and Quantum Gravity
- Pub Date:
- September 1996
- DOI:
- 10.1088/0264-9381/13/9/004
- arXiv:
- arXiv:hep-th/9603021
- Bibcode:
- 1996CQGra..13.2361A
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 29 pages, plain-tex. In this revised version, the analysis of the self-adjointness problem with Barvinsky boundary conditions has been amended. For this purpose, section 4 has been completely revised, and a new section has been added. The literature on the axial gauge is also described