Contents

Abstract. We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation in a vector bundle and the method of second quantization leads to a symplectic vector space (V, ω) and a corresponding CCR representation for the bosonic components and a CAR representation for the fermionic part. The solution space of the Wheeler-DeWitt equation is invariant under gauge transformations and under isometries in the spacelike base space S0 of a given Riemann-ian metric ρij. We also define a net of local subalgebras which satisfy four of the Haag-Kastler axioms