p-Mechanics and De Donder-Weyl Theory
Quantum Physics
2015-12-25 v2
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 M\"obius transformation, Dirac operator
Cite
@article{arxiv.quant-ph/0306101,
title = {p-Mechanics and De Donder-Weyl Theory},
author = {Vladimir V. Kisil},
journal= {arXiv preprint arXiv:quant-ph/0306101},
year = {2015}
}
Comments
LaTeX, 8 pages, no figures