Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems

Details Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems

1997-03-07

arxiv.org/abs/gr-qc/9703021v1

Phys.Rev. D56 (1997) 6247-6257

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages ReVTeX

Scientific paper

10.1103/PhysRevD.56.6247

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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