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arXiv · hep-th/9810165

DeDonder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory

I. V. Kanatchikov
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Abstract

A quantization of field theory based on the DeDonder-Weyl covariant Hamiltonian formulation is discussed. A hypercomplex extension 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 of differential forms put forward for the DeDonder-Weyl formulation earlier. The proposed covariant hypercomplex Schrödinger equation is shown to lead in the classical limit to the DeDonder-Weyl Hamilton-Jacobi equation and to obey the Ehrenfest principle in the sense that the DeDonder-Weyl canonical field equations are satisfied for the expectation values of properly chosen operators.

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I. V. Kanatchikov. 1998-10-21. DeDonder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory. https://doi.org/10.1016/s0034-4877(99)80024-x

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