p-Mechanics and De Donder-Weyl Theory

Vladimir V. Kisil

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p-Mechanics and De Donder-Weyl Theory

Vladimir V. Kisil

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Abstract

The orbit method of Kirillov is used to derive the p-mechanical brackets [quant-ph/0212101]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder-Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with Galilean. Keywords: Classic and quantum mechanics, Moyal brackets, Poisson brackets, commutator, Heisenberg group, orbit method, deformation quantisation, representation theory, De Donder-Weyl field theory, Galilean group, Clifford algebra, conformal Möbius transformation, Dirac operator

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Vladimir V. Kisil. 2003-07-04. p-Mechanics and De Donder-Weyl Theory. https://arxiv.org/abs/quant-ph/0306101

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