Loop quantum gravity coupled to a scalar field

Understand

We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field.

• Several new results for loop quantum gravity are obtained: (i) a Hilbert space for the gravity-matter system and a non-standard representation of the scalar field thereon is constructed, (ii) a new operator for the scalar constraint of the coupled system is defined and investigated, (iii) methods for solving the constraint are developed.
• Commutators of the new constraint do not vanish, but seem to reproduce a part of the Dirac algebra.
• This, however, poses problems for finding solutions.