Year: 2005
Type: article
Abstract: We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schr\"odinger equation, and quantum gravitational correction terms to this Schr\"odinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many-fingered) local time parameter has to be present on super Riem $\ensuremath{\Sigma}$ (the space of all possible tetrad and gravitino fields), (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early Universe. The physical meaning of these equations and results, in particular, the similarities to and differences from the pure bosonic case, are discussed.
Authors: Claus Kiefer, Tobias Lück, Paulo Moniz
Institutions: University of Cologne, Queen Mary University of London
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2018125875