Knot polynomial states of quantum gravity in terms of loops and extended loops: Some remarks

In this paper we review the status of several solutions to all the constraints of quantum gravity that have been proposed in terms of loops and extended loops, based on knot polynomials. We discuss pitfalls of several of the results, and in particular the issues of covariance and regularization of the constraints in terms of extended loops. We also propose a formalism for thickened out loops, which does not face the covariance problems of extended loops and may allow to regularize expressions in a consistent manner. © 1995 American Institute of Physics