How can Supersymmetry be used in a Simple Quantum Cosmological Model
The general theory of N=1 supergravity with supermatter is applied to a Bianchi type IX diagonal model. The supermatter is constituted by a complex scalar eld and its spin-1 2 fermionic partners. The Lorentz invariant Ansatz for the wave function of the universe, , is taken to be as simple as possible in order to obtain new solutions. The wave function has a simple form when the potential energy term is set to zero. However, neither the wormhole or the Hartle-Hawking state could be found. The Ansatz for used in this paper is constrasted with the more general framework of R. Graham and A. Csordd as. A quantum gravity theory constitutes a desirable goal in theoretical physics as it could lead to a proper uniication of all know interactions within a quantum mechanical point of view. The inclusion of supersymmetry in quantum gravity and cosmology allowed a number of interesting results and conclusions to be achieved in the last ten years or so. Several approaches may be found in the literature, namely the triad ADM canonical formulation, the ?model supersymmetric extension in quantum cosmology, and another approach based on Ashtekar variables (see ref. 1,2] and references therein). The canonical quantization framework of N=1 (pure) supergravity was presented in ref. 3]. It has been pointed out that it would be suucient, in nding a physical state, to solve the Lorentz and supersymmetry constraints of the theory due to the algebra of constraints of the theory. The presence of local supersymmetry could also contribute to the removal of divergences. Moreover, the supersymmetry constraints provide a Dirac-like square root of the second order Wheeler-DeWitt equation. Hence, we were led to solve instead a set of coupled rst-order diierential equations which ought to satisfy. As a result, simple forms for were obtained, representing states such as the Hartle-Hawking (no-boundary) solution or the (ground state) wormhole solution 4]. Most of these results seemed then to emphasize a particular basic track, where a Dirac-like square-root structure is used to obtain directly any physical states. However, this back to basics line*** is not the whole story. On the one hand, it seemed that the gravitational and gravitino modes that were allowed to be excited