Supersymmetric Quantum Cosmology --- Shaken not stirred

The canonical quantization of $N=1$ and $N=2$ supergravity theories is reviewed in this report. A special emphasis is given to the topic of supersymmetric Bianchi class-A and FRW minisuperspaces, namely in the presence of supermatter fields. The quantization of the general theory (including supermatter) is also contemplated. The issue of quantum physical states is subsequently analysed. A discussion on further research problems still waiting to be addressed is included. An extensive and updated bibliography concludes this review.Comment: 50 pages, plain LaTeX, Topical Review for International Journal of Modern Physics-A, Revised version, style improved, new references and updated, some issues clarifie

Conserved Currents in Supersymmetric Quantum Cosmology?

In this paper we investigate whether conserved currents can be sensibly defined in supersymmetric minisuperspaces. Our analysis deals with k=1 FRW and Bianchi class--A models. Supermatter in the form of scalar supermultiplets is included in the former. Moreover, we restrict ourselves to the first-order differential equations derived from the Lorentz and supersymmetry constraints. The ``square-root'' structure of N=1 supergravity was our motivation to contemplate this interesting research. We show that conserved currents cannot be adequately established except for some very simple scenarios. Otherwise, conservation equations may only be obtained from Wheeler-DeWitt--like equations, which are derived from the supersymmetric algebra of constraints. Two appendices are included. In appendix A we describe some interesting features of quantum FRW cosmologies with complex scalar fields when supersymmetry is present. In particular, we explain how the Hartle-Hawking state can now be satisfactorily identified. In appendix B we initiate a discussion about the retrieval of classical properties from supersymmetric quantum cosmologies.Comment: 16 pages, LaTeX (plain), Extended version of a report written for the 1996 Awards for Essays on Gravitation, main text re-written and reduced, includes appendix A (about complex scalr fields in quantum cosmology) and B (about retrieval of classical features in supersymmetric quantum cosmology), references are update

Wave Function of a Supersymmetric FRW Model with Vector Fields

A specific Friedmann-Roberstson-Walker (FRW) model derived from the theory of N=1 supergravity with gauged supermatter is considered in this paper. The supermatter content is restricted to a vector supermultiplet. The corresponding Lorentz and supersymmetry quantum constraints are then derived. Non-trivial solutions are subsquently found. A no-boundary solution is identified while another state may be interpreted as a wormhole solution.Comment: 14 pages, plain LaTe