One-Loop Amplitudes in Euclidean Quantum Gravity

Details One-Loop Amplitudes in Euclidean Quantum Gravity One-Loop Amplitudes in Euclidean Quantum Gravity

1995-04-12

arxiv.org/abs/gr-qc/9504016v1

Phys.Rev. D52 (1995) 3457-3465

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, plain TeX, no figures

Scientific paper

10.1103/PhysRevD.52.3457

This paper studies the linearized gravitational field in the presence of boundaries. For this purpose, $\zeta$-function regularization is used to perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes in the case of flat Euclidean four-space bounded by a three-sphere. On choosing the de Donder gauge-averaging term, the resulting $\zeta(0)$ value is found to agree with the space-time covariant calculation of the same amplitudes, which relies on the recently corrected geometric formulas for the asymptotic heat kernel in the case of mixed boundary conditions. Two sets of mixed boundary conditions for Euclidean quantum gravity are then compared in detail. The analysis proves that one cannot restrict the path-integral measure to transverse-traceless perturbations. By contrast, gauge-invariant amplitudes are only obtained on considering from the beginning all perturbative modes of the gravitational field, jointly with ghost modes.

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