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A new representation of Quantum Gravity is developed. This formulation isbased on an extension of the group of loops. The enlarged group, that we callthe Extended Loop Group, behaves locally as an infinite dimensional Lie group.Quantum Gravity can be realized on the state space of extended loop dependentwavefunctions. The extended representation generalizes the loop representationand contains this representation as a particular case. The resultingdiffeomorphism and hamiltonian constraints take a very simple form and allow toapply functional methods and simplify the loop calculus. In particular we showthat the constraints are linear in the momenta. The nondegenerate solutionsknown in the loop representation are also solutions of the constraints in thenew representation. The practical calculation advantages allows to find a newsolution to the Wheeler-DeWitt equation. Moreover, the extended representationputs in a precise framework some of the regularization problems of the looprepresentation. We show that the solutions are generalized knot invariants,smooth in the extended variables, and any framing is unnecessary.Comment: 27 pages, report IFFC/94-1

Extended loop representation of quantum gravity