Reduced phase space approach to Kasner universe and the problem of time in quantum theory

Details Reduced phase space approach to Kasner universe and the problem of time in quantum theory Reduced phase space approach to Kasner universe and the problem of time in quantum theory

2011-05-30

arxiv.org/abs/1105.6030v3

Class. Quantum Grav. 29 (2012) 075008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages

Scientific paper

We apply the reduced phase space quantization to the Kasner universe. We construct the kinematical phase space, find solutions to the Hamilton equations of motion, identify Dirac observables and arrive at physical solutions in terms of Dirac observables and an internal clock. We obtain the physical Hilbert space, which is the carrier space of the self-adjoint representation of the Dirac observables. Then we discuss the problem of time. We demonstrate that the inclusion of evolution in a gravitational system, at classical level as well as at quantum level, leads respectively to canonically and unitarily inequivalent theories. The example of Hubble operator in two different clock variables and with two distinct spectra is given.

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