Conserved quantities in isotropic loop quantum cosmology

Naval Academy Preparatory School - 197 Elliot Street, Newport, RI 02841, USA

^a cartin@naps.edu

Received: 22 December 2011
Accepted: 10 April 2012

Abstract

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.