DE DONDER-WEYL THEORY AND A HYPERCOMPLEX EXTENSION 0F QUANTUM MECHANICS TO FIELD THEORY

A quantization of field theory based on the De Donder-Weyl (DW) covariant Harniltonian formulation is discussed. A hypercomplex extensnin of quantum mechanics, in which the space-time Clifford algebra replaces that of the complex numbers, appears as a result of quantization of Poisson brackets on differential forms which were put forward for the DW theory earlier. The proposed covariant hypercomplex Schrodinger equation is shown to lead in the classical limit to the DW Hamilton-Jacobi equation and to obey the Ehrenfest principle in the sense that the DW canonical field equations are satisfied for expectation values of properly chosen operators.