Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1993-09-09
Phys.Lett. B318 (1993) 115-121
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, Report DESY 93-125, THU-93/19
Scientific paper
10.1016/0370-2693(93)91793-M
To clarify some issues raised by D'Eath's recent proposal for the physical states of $N=1$ supergravity in four dimensions, we study pure (topological) $N=2$ supergravity in three dimensions, which is formally very similar, but much easier to solve. The wave functionals solving the quantum constraints can be understood in terms of arbitrary functions on the space of moduli and supermoduli, which is not Hausdorff. We discuss the implications for the wave functionals and show that these are not amenable to expansions in fermionic coordinates, but can serve as lowest-order solutions to the quantum constraints in an expansion in $\hbar$ in more realistic theories.
Matschull Hans-Juergen
Nicolai Hermann
Wit Bernard de
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