A group theoretical approach to the canonical quantisation of gravity. II. Unitary representations of the canonical group

Abstract

For pt.I see ibid., vol.1, p.621-32, 1984. Unitary representations of the canonical group C for quantum gravity, discussed in an earlier paper, are studied producing concrete operator realisations of the basic canonical fields eAB, pi CD of the theory together with its spatial diffeomorphism group covariance. The appropriate state functionals are concentrated on distributional triads and not smooth ones. In addition, for a class of these representations the distributional triads are also degenerate, a feature does not appear for the conventional canonical commutation relations and the weak-field perturbation framework.