Quantization of a Friedmann-Robertson-Walker Model with Gauge Fields in N=1 Supergravity

The purpose of this paper is to investigate a specific FRW model derived from the theory of N=1 supergravity with gauged supermatter. The supermatter content is restricted to a vector supermultiplet. This objective is particularly worthwhile. In fact, it was pointed in ref. ({\em Class. Quantum Grav. {\bf 12} {\rm (} {\rm 1995} {\rm )} {\rm 1343}}) that $\mathrm{\Psi }=0$ was the only allowed quantum state for N=1 supergravity with {\em generic} gauged supermatter subject to suitable FRW ans"atze. The ans"atze employed here for the physical variables was presented in the above reference. The corresponding Lorentz and supersymmetry quantum constraints are then derived. Non-trivial solutions are subsquently found. A no-boundary solution is identified while another state may be interpreted as a wormhole solution. In addition, the usefulness and limitations of the ans"atze are addressed. The implications of the ans"atze with respect to the allowed quantum states are also discussed.