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arXiv · quant-ph/0402035

p-Mechanics and Field Theory

Vladimir V. Kisil
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Abstract

The orbit method of Kirillov is used to derive the p-mechanical brackets [math-ph/0007030, 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. 2005-06-09. p-Mechanics and Field Theory. https://doi.org/10.1016/s0034-4877(05)80068-0

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