Quantising the conformal degree of freedom

The basic problem in quantising gravity is that we do not know how to quantise a theory described by an arbitrary lagrangian. The only systematic method available - based on perturbation theory - works only for a special type of lagrangians ('perturbatively renormalizable'). Unfortunately, gravitational lagrangian does not belong to this particular class; the straight path to quantising is blocked. One of three different attitudes to this situation: that is, to develop a 'partial quantisation' by quantising some selected modes of gravity in a non-perturbative manner is discussed. Quantum cosmology, which tries to assign a quantum mechanical meaning to classical cosmological solutions, is explained. The problems of quantising gravity are described and one approach to solving these problems by quantising the conformed mode, is described. (author)