Abstract
A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant “hyperbolic” models such as minisuperspace quantum cosmology. The connection with sum-over-histories constructions is exhibited and the physical equivalence or inequivalence of different such schemes is analyzed. The discussion focuses on comparing constructions based on the Klein-Gordon product with those based on the induced (also known as Rieffel, refined algebraic, group averaging, or spectral analysis) inner product. It is shown that the Klein-Gordon and induced products can be simply related for the models of interest. This fact is then used to establish isomorphisms between certain decoherence schemes based on these products.
- Received 13 May 1997
DOI:https://doi.org/10.1103/PhysRevD.56.6247
©1997 American Physical Society