Towards the Born-Weyl Quantization of Fields

Details Towards the Born-Weyl Quantization of Fields Towards the Born-Weyl Quantization of Fields

1997-12-31

arxiv.org/abs/quant-ph/9712058v1

Int.J.Theor.Phys. 37 (1998) 333-342

Physics

Quantum Physics

12pp, LaTeX2e. Talk at "Quantum Structures-96", Berlin, Aug. 1996. To appear in Int. J. Theor. Phys. (1998), January

Scientific paper

Elements 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 Schr\"odinger 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 Schr\"odinger picture in quantum field theory is outlined.

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