Supersymmetric quantum matrix cosmology

Abstract

We exhibit a relation between the SU(2) invariant matrix model arising from the quantization of the 11-dimensional supermembrane in the light cone gauge and supersymmetric quantum cosmology. We use a Dirac-like gamma matrix representation for the fermionic degrees of freedom and find explicit solutions to reduced lower dimensional SU(2) matrix models for the zero energy states. One of the solutions we encounter in the matrix model resembles exactly a wave function found independently in the context of SUSY quantum cosmology; this allows us to give these regularized models a physical meaning and shows a direct relation between the SU(2) matrix model and SUSY quantum cosmology.