Comment on the transition amplitude for toy universe models

Abstract

The parametrized system called ``ideal clock'' is turned into an ordinary gauge system and quantized by means of a path integral in which canonical gauges are admissible. Then the possibility of applying the results to obtain the transition amplitude for empty minisuperspaces, and the restrictions arising from the topology of the constraint surface, are studied by matching the models with the ideal clock. A generalization to minisuperspaces with true degrees of freedom is also discussed.