Conserved quantities in isotropic loop quantum cosmology
Naval Academy Preparatory School - 197 Elliot Street, Newport, RI 02841, USA
Accepted: 10 April 2012
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 wave function 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.
PACS: 04.60.Pp – Loop quantum gravity, quantum geometry, spin foams / 98.80.Qc – Quantum cosmology / 02.30.Xx – Calculus of variations
© EPLA, 2012