Diffeomorphism-invariant quantum field theories of connections in terms ofwebs

In the canonical quantization of gravity in terms of the Ashtekar variables one uses paths in the 3-space to construct the quantum states. Usually, on e restricts oneself to families of paths admitting only a finite number of isolated intersections. This assumption implies a limitation on the diffeom orphisms invariance of the introduced structures. In this work, using the p revious results of Baez and Sawin, we extend the existing results to a theo ry admitting all the possible piecewise-smooth finite paths and loops. In p articular, we (a) characterize the spectrum of the Ashtekar-Isham configura tion space, (b) introduce spin-web states, a generalization of the spin net work states, (c) extend the diffeomorphism averaging to the spin-web states and derive a large class of diffeomorphism-invariant states and finally (d ) extend the 3-geometry operators and the Hamiltonian operator.