  Quantization of gravity is discussed in the context of field quantization
based on an analogue of canonical formalism (the De Donder-Weyl canonical
theory) which does not require the space+time decomposition. Using Horava's
(1991) De Donder-Weyl formulation of General Relativity we put forward a
covariant generalization of the Schr\"odinger equation for the wave function of
space-time and metric variables and a supplementary ``bootstrap condition''
which self-consistently incorporates the classical background space-time
geometry as a quantum average and closes the system of equations. Some open
questions for further research are outlined.
