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A new representation for canonical gravity and supergravity is presented,which combines advantages of Ashtekar's and the Wheeler~DeWitt representation:it has a nice geometric structure and the singular metric problem is absent. Aformal state functional can be given, which has some typical features of avacuum state in quantum field theory. It can be canonically transformed intothe metric representation. Transforming the constraints too, one recovers theWheeler~DeWitt equation up to an anomalous term. A modified Dirac quantizationis proposed to handle possible anomalies in the constraint algebra.Comment: 28 pages, LaTe

New representation and a vacuum state for canonical quantum gravity