Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity

Details Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity

1995-02-09

arxiv.org/abs/gr-qc/9502023v2

Phys.Rev. D52 (1995) 6947-6964

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

32 pages, latex. The revision is a more general treatment of the regulator. Local constraints are now derived from a requireme

Scientific paper

10.1103/PhysRevD.52.6947

We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand $\exp[ \sqrt{i} S ]$ rather than the familiar Feynman expression $\exp[ i S ]$, and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions.

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