Supersymmetric quantum matrix cosmology. (English) Zbl 1329.83224
Summary: We exhibit a relation between the \(\mathrm{SU}(2)\) 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 \(\mathrm{SU}(2)\) 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 \(\mathrm{SU}(2)\) matrix model and SUSY quantum cosmology.
MSC:
| 83F05 | Relativistic cosmology |
| 83C45 | Quantization of the gravitational field |
| 81V22 | Unified quantum theories |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83E50 | Supergravity |
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