Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-09-02
Phys.Rev. D73 (2006) 024011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
45 pages, RevTex. Version 2. Substantial rewriting of Section 9 correcting earlier errors
Scientific paper
10.1103/PhysRevD.73.024011
The decoherent histories approach to quantum theory is applied to a class of reparametrization invariant models, which includes systems described by the Klein-Gordon equation, and by a minisuperspace Wheeler-DeWitt equation. A key step in this approach is the construction of class operators characterizing the questions of physical interest, such as the probability of the system entering a given region of configuration space without regard to time. In non-relativistic quantum mechanics these class operators are given by time-ordered products of projection operators. But in reparametrization invariant models, where there is no time, the construction of the class operators is more complicated, the main difficulty being to find operators which commute with the Hamiltonian constraint (and so respect the invariance of the theory). Here, inspired by classical considerations, we put forward a proposal for the construction of such class operators for a class of reparametrization-invariant systems. They consist of continuous infinite temporal products of Heisenberg picture projection operators. We investigate the consequences of this proposal in a number of simple models and also compare with the evolving constants method.
Halliwell Jonathan J.
Wallden Petros
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