Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems
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 (a.k.a. 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.
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Cite
@article{arxiv.gr-qc/9703021,
title = {Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems},
author = {James B. Hartle and Donald Marolf},
journal= {arXiv preprint arXiv:gr-qc/9703021},
year = {2016}
}
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21 pages ReVTeX