Dirac-like formulation of quantum supersymmetric cosmology

Details Dirac-like formulation of quantum supersymmetric cosmology Dirac-like formulation of quantum supersymmetric cosmology

Jan 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phrvd..57.1015o&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 57, Issue 2, 15 January 1998, pp.1015-1026

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14

Lower Dimensional Models, Minisuperspace Models, Supergravity, Supersymmetric Models

Scientific paper

We present a Dirac-like framework for quantum cosmology. This is achieved by representing the gravitino field components, analogously to the Dirac equation, as matrices. In particular, we work out the Bianchi type IX diagonal model. The Lorentz constraints Jαβ can then be applied explicitly on the wave function, which results in a 64-component vector, without any particular assumption on its expansion in fermionic (and bosonic) variables. The resulting wave function has only two nonvanishing components. Hence, the Dirac-like structure of the SA constraints manifests itself in a system of equations for these two functions, where the ``potential'' plays the role of the charge in Dirac's theory. We exhibit two solutions whose explicit form is determined by the chosen factor ordering. The proposed construction can be systematically extended to other cosmologies and the inclusion of matter.

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