  We propose a manifestly covariant canonical method of field quantization
based on the classical De Donder-Weyl covariant canonical formulation of field
theory. Owing to covariance, the space and time arguments of fields are treated
on an equal footing. To achieve both covariance and consistency with standard
noncovariant canonical quantization of fields in Minkowski spacetime, it is
necessary to adopt a covariant Bohmian formulation of quantum field theory. A
preferred foliation of spacetime emerges dynamically owing to a purely quantum
effect. The application to a simple time-reparametrization invariant system and
quantum gravity is discussed and compared with the conventional noncovariant
Wheeler-DeWitt approach.
