Solutions to the Wheeler DeWitt Constraint of Canonical Gravity Coupled to Scalar Matter Fields
H.-J. Matschull
TL;DR
This paper presents formal solutions to the Wheeler DeWitt constraint in canonical gravity with scalar matter fields, extending known Wilson loop solutions using Ashtekar's variables and loop parametrization.
Contribution
It introduces a new class of solutions to the Wheeler DeWitt equation in the context of scalar matter coupled to gravity, utilizing Ashtekar's variables and loop techniques.
Findings
Solutions parametrized by loops in the hypersurface
Extensions of Wilson loop solutions by Jacobson, Rovelli, and Smolin
Formal solutions in the presence of scalar matter fields
Abstract
It is shown that the Wheeler DeWitt constraint of canonical gravity coupled to Klein Gordon scalar fields and expressed in terms of Ashtekar's variables admits formal solutions which are parametrized by loops in the three dimensional hypersurface and which are extensions of the well known Wilson loop solutions found by Jacobson, Rovelli and Smolin.
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