Conserved Currents in Supersymmetric Quantum Cosmology?

Details Conserved Currents in Supersymmetric Quantum Cosmology? Conserved Currents in Supersymmetric Quantum Cosmology?

1996-06-17

arxiv.org/abs/gr-qc/9606047v2

Int.J.Mod.Phys. D6 (1997) 625-641

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, LaTeX (plain), Extended version of a report written for the 1996 Awards for Essays on Gravitation, main text re-writ

Scientific paper

10.1142/S0218271897000388

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.

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