The space of states of quantum gravity in terms of loops and extended loops: some remarks

This article reviews the status of several solutions to all the constraints of quantum gravity that have been proposed in terms of loops and extended loops. We discuss pitfalls of several of the results and in particular discuss 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.