Path Integrals and Instantons in Quantum Gravity

Details Path Integrals and Instantons in Quantum Gravity Path Integrals and Instantons in Quantum Gravity

1996-02-12

arxiv.org/abs/gr-qc/9602019v2

Phys.Rev.D53:6979-6990,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, ReVTeX, minor changes: clarifying Comments and references added

Scientific paper

10.1103/PhysRevD.53.6979

While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and preserves the systems' explicit reparametrization invariance. In the following study, this canonical formalism is used to derive a path integral for quantum minisuperspace models. As it comes from a well-defined canonical starting point, the measure and contours of integration are specified by this construction. The properties of the resulting path integral are analyzed, both exactly and in the semiclassical limit. Particular attention is paid to the role of the (unbounded) Euclidean action and Euclidean instantons are argued to contribute as $e^{-|S_E|/\hbar}$.

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