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Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems

James B. Hartle·Donald Marolf
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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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BibTeXRIS

James B. Hartle, Donald Marolf. 1997-03-07. Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems. https://doi.org/10.1103/physrevd.56.6247

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