Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2012-04-16
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
6 pages, to be published in Europhysics Letters
Scientific paper
We develop an action principle for those models arising from isotropic loop quantum cosmology, and show that there is a natural conserved quantity $Q$ for the discrete difference equation arising from the Hamiltonian constraint. This quantity $Q$ relates the semi-classical limit of the wavefunction at large values of the spatial volume, but opposite triad orientations. Moreover, there is a similar quantity for generic difference equations of one parameter arising from a self-adjoint operator.
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