Super-Minisuperspace and New Variables

Abstract

We consider the specialization to spatially homogenous solutions of the Jacobson formulation of N=1 canonical supergravity in terms of Ashtekar's new variables. We find that the classical Poisson algebra of the supersymmetry constraints is preserved by this specialization only for Bianchi type A models. The quantization of supersymmetric Bianchi type A models is carried out in the triad representation. We find the physical states of this quantum theory. Since we are missing a suitable inner product on these physical states, our results are only formal.

16 pages, CIEA-GR-9401

References in corpus (4)

• Supersymmetric Bianchi class A models
• Unique determination of an inner product by adjointness relations in the algebra of quantum observables
• Degenerate Extensions of General Relativity
• On the Constraint Algebra of Degenerate Relativity

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• Quantum states on supersymmetric minisuperspace with a cosmological constant
• D = 1 supergravity and quantum cosmology
• Supersymmetry and Quantum Cosmology
• Supersymmetric Barotropic FRW Model and Dark Energy