A group theoretical approach to the canonical quantisation of gravity. I. Construction of the canonical group

An approach to quantisation in terms of a transitive group of symplectic transformations of the classical phase space is discussed. This is applied to general relativity where the phase space is nonlinear and it is shown that the appropriate canonical algebra (i.e. the analogue of the canonical commutation relations for the case of a linear phase space) is that of the affine commutation relations.