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The general theory of N = 1 supergravity with supermatter is studied using acanonical approach. The supersymmetry and gauge constraint generators arefound. The framework is applied to the study of a Friedmann minisuperspacemodel. We consider a Friedmann k = + 1 geometry and a family of spin-0 as wellas spin-1 gauge fields together with their odd (anti-commuting) spin-1/2partners. The quantum supersymmetry constraints give rise to a set offirst-order coupled partial differential equations for the components of thewave function. As an intermediate stage in this project, we put both the spin-1field and its fermionic partner equal to zero. The physical states of oursimplified model correspond effectively to those of a mini-superspace quantumcosmological model possessing N=4 local supersymmetry coupled to complexscalars with spin-1/2 partners. The different supermatter models are given byspecifying a K\"ahler metric for the scalars; the allowed quantum states thendepend on the K\"ahler geometries. For the cases of spherically symmetric andflat K\"ahler geometries we find the general solution for the quantum statewith a very simple form. However, although they allow a Hartle-Hawking state,they do not allow a wormhole state.Comment: 24 pages, DAMTP R94/2

QUANTIZATION OF A LOCALLY SUPERSYMMETRIC FRIEDMANN MODEL IN THE PRESENCE OF SUPERMATTER