Abstract
Recently, using Ashtekar's new canonical formulation of general relativity, a large class of solutions of the quantum hamiltonian constraint were found by Jacobson and Smolin. These solutions are the traces of the holonomy for Ashtekar's connection that are based on differentiable loops. In this paper, additional solutions of the quantum hamiltonian constraint are described. These new solutions also involve the holonomy, but are based on multiple loops that intersect at a point. It is shown that no solutions exist for three intersecting loops that have more than two linearly independent tangent vectors at the intersection point.
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