Document Type
Article
Publication Date
10-26-1992
Abstract
We find a consistent formulation of the constraints of quantum gravity with a cosmological constant in terms of the Ashtekar new variables in the connection representation, including the existence of a state that is a solution to all the constraints. This state is related to the Chern-Simons form constructed from the Ashtekar connection and has an associated metric in space-time that is everywhere nondegenerate. We then transform this state to the loop representation and find solutions to all the constraint equations for intersecting loops. These states are given by suitable generalizations of the Jones knot polynomial for the case of intersecting knots. These are the first physical states of quantum gravity for which an explicit form is known both in the connection and loop representations. Implications of this result are also discussed. © 1992.
Publication Source (Journal or Book title)
Nuclear Physics, Section B
First Page
587
Last Page
603
Recommended Citation
Brügmann, B., Gambini, R., & Pullin, J. (1992). Jones polynomials for intersecting knots as physical states of quantum gravity. Nuclear Physics, Section B, 385 (3), 587-603. https://doi.org/10.1016/0550-3213(92)90060-O