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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. [ABSTRACT FROM AUTHOR]

It is shown that like the Bianchi I, V and IX models, a Kantowski–Sachs cosmological model also allows unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of anisotropy. Non-unitarity, if there is any, cannot escape notice here, as the evolution is studied against a properly oriented time parameter fixed by the evolution of the fluid. Furthermore, we have constructed a wave packet by superposing different energy eigenstates, thereby establishing unitarity in a non-trivial way, which is a stronger result than an energy eigenstate trivially giving a time independent probability density. For , we have proved that the Hamiltonian admits a self-adjoint extension under a reasonable assumption, using a standard theorem. This consolidates the fact that the problem of non-unitarity cannot be a generic problem of anisotropy. [ABSTRACT FROM AUTHOR]

We construct a new vacuum and representation for loop quantum gravity. Because the new vacuum is based on BF theory, it is physical for (2+1)-dimensional gravity, and much closer to the spirit of spin foam quantization in general. To construct this new vacuum and the associated representation of quantum observables, we introduce a modified holonomy–flux algebra that is cylindrically consistent with respect to the notion of refinement by time evolution suggested in Dittrich and Steinhaus (2013 arXiv:1311.7565). This supports the proposal for a construction of the physical vacuum made in Dittrich and Steinhaus (2013 arXiv:1311.7565) and Dittrich (2012 New J. Phys.14 123004), and for (3+1)-dimensional gravity. We expect that the vacuum introduced here will facilitate the extraction of large scale physics and cosmological predictions from loop quantum gravity. [ABSTRACT FROM AUTHOR]