Canonical quantisation of a spherically symmetric, massless scalar field interacting with gravity in (2+1) dimensions

A spherically symmetric, massless scalar field is allowed to interact with gravity via Einstein's field equations in a three-dimensional spacetime. The imposition of spherical symmetry makes this a minisuperspace model. The model is quantised by splitting spacetime into space and time, and then imposing canonical commutation relations. A comparison is made of such minisuperspace models with models with no imposed symmetries in flat spacetime. The two main points made about the model are: the quantised model is found to violate the principle of microcausality, and the vacuum fluctuations of the metric are found to become infinite even for a finite-sized smearing volume. (author)