Comparing formulations of generalized quantum mechanics for reparametrization-invariant systems

James B. Hartle and Donald Marolf
Phys. Rev. D 56, 6247 – Published 15 November 1997
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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 (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

Authors & Affiliations

James B. Hartle

  • Institute of Theoretical Physics, University of California, Santa Barbara, California 93106

Donald Marolf

  • 201 Physics Building, Syracuse University, Syracuse, New York 13244

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Issue

Vol. 56, Iss. 10 — 15 November 1997

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