Igor Kanatchikov (UK): De Donder‐Weyl Hamiltonian theory and precanonical quantization: an untrodden path to quantization of fields and gravity

I will discuss (I) the De Donder‐Weyl (DW) Hamiltonian and Hamilton‐Jacobi formulation of classical fields and the underlying mathematical structures which can be used for quantization (the polysymplectic structure and the Poisson‐Gerstenhaber brackets), (II) a field quantization based on those structures (precanonical quantization) which leads to a hypercomplex rather than infinite‐dimensional generalization of quantum theory as a description of quantum fields, (III) examples of precanonical quantization of a nonlinear scalar field on flat and curved background, and the pure Yang‐Mills field, (IV) the consistency of precanonical quantization with the Ehrenfest theorem, (V) the relation to the standard QFT in the functional Schrödinger representation, which appears as a singular limiting case, (VI) precanonical quantization of general relativity in vielbein Palatini formulation and the spin‐connection foam picture of quantum geometry of space‐time it leads to.