2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100106Elements of the quantization in field theory based on the covariant polymomentum Hamiltonian formalism (the De Donder-Weyl theory), a possibility of which was originally discussed in 1934 by Born and Weyl, are developed. The approach is based on a recently proposed graded Poisson bracket on differential forms in field theory (see e.g. hep-th/9709229). A covariant analogue of the Schrödinger equation for a hypercomplex wave function on the space of field and space-time variables is put forward. It is shown to lead to the De Donder-Weyl Hamilton-Jacobi equations in quasiclassical limit. A possible relation to the functional Schrödinger picture in quantum field theory is outlined.12pp, LaTeX2e. Talk at "Quantum Structures-96", Berlin, Aug. 1996. To appear in Int. J. Theor. Phys. (1998), JanuaryQuantum PhysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - TheoryMathematical Physicstext