Path Integrals and Instantons in Quantum Gravity

TL;DR

This paper develops a canonical path integral formulation for quantum minisuperspace models in quantum gravity, analyzing its properties and the role of Euclidean instantons in the semiclassical limit.

Contribution

It introduces a canonical derivation of the path integral for minisuperspace models that preserves reparametrization invariance and specifies the measure and contours of integration.

Findings

Path integral derived from canonical formalism with explicit measure

Analysis of path integral properties both exactly and semiclassically

Euclidean instantons contribute as exponential factors involving Euclidean action

Abstract

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 $e^{-|S_E|/\hbar}$.