The Superspace of Geometrodynamics

Wheeler’s Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity. PACS 04.60.-m · 04.60.Ds · 02.40.-k Mathematics Subject Classification (2000) 83C45 · 57N10 · 53D20 “The stage on which the space of the Universe moves is certainly not space itself. Nobody can be a stage for himself; he has to have a larger arena in which to move. The arena in which space does its changing is not even the spacetime of Einstein, for space-time is the history of space changing with time. The arena must be a larger object: superspace. . . It is not endowed with three or four dimensions—it’s endowed with an infinite number of dimensions.” (J.A. Wheeler: Superspace, Harper’s Magazine, July 1974, p. 9)