Abstract
The formulation of path integrals in terms of pseudomeasures by Cecile DeWitt-Morette is extended to infinite-dimensional state-spaces and to the state spaces dual to nuclear spaces appropriate to second-quantisation. In both cases a “distribution” formulation is given to allow a subsequent extension to manifolds. It is shown that the resulting theory is “correct” in that it can give rise to a wave function on state space which obeys a Schrödinger equation in appropriate circumstances. The corresponding state manifolds for quantum gravity are then defined, and the conditions under which the theory extends to them are discussed. it is shown in an appendix that the Riemannian metric required by the theory exists on one of the types of state manifold for a wide class of cases.
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Communicated by R. Geroch
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Clarke, C.J.S. The application of Dewitt-Morette path integrals to general relativity. Commun.Math. Phys. 56, 125–146 (1977). https://doi.org/10.1007/BF01611499
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DOI: https://doi.org/10.1007/BF01611499