A GENERALLY COVARIANT QUANTUM-FIELD THEORY AND A PREDICTION ON QUANTUM MEASUREMENTS OF GEOMETRY

We define a generally covariant quantum field theory with an infinite number of degrees of freedom. This is obtained by combining the Husain-Kuchar model, the Loop Representation, the idea of defining diffeomorphism invariant observables in terms of material reference systems, and the Ashtekar-Isham C-algebra representation theory. The theory can be seen as a c --> 0 limit of general relativity coupled with material objects. The construction of the quantum theory can be completed to the point where physical expectation values can be computed, and quantitative physical predictions about gauge-invariant observables can be made within the model. The first physical result that we obtain is that the area of physical surfaces (defined by the matter coupled to the gravitational field) is quantized in units of A0 = HBARG/2c3. This result was anticipated as a non-gauge-invariant result within quantum general relativity, but it becomes a definite result in the present model. It supports the prediction that the quantization of the area is a genuine physical effect. We discuss the meaning of this prediction in terms of quantum measurement theory, and the assumptions from which this prediction follows.