MG11 
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SUPERSIMMETRIC QUANTUM COSOLOGY: MATRIX APPROACH

In 1987 Mac\'{\i}as, Obreg\'on and Ryan introduced the supersymmetric quantum cosmology approach by applying (N=1) supergravity to quantum minisuperspaces in order to obtain the square root of the Wheeler--DeWitt equation, which governs the evolution of the quantum cosmological models in the standard approach, by means of a matrix representation for the gravitino field. In this talk I will review the further developments of this approach and show that there exist no physical states in the minisuperspace sector of the supersymmetric quantum cosmology. Moreover, I show also that there exist physical states in its midisperspace sector provided that one considers an infinite number of gravitino modes, in acordance with results of Carrol, Freedman, Ort\'{\i}z, and Page.