p-Mechanics and Field Theory
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 M\"obius transformation, Dirac operator.
Cite
@article{arxiv.quant-ph/0402035,
title = {p-Mechanics and Field Theory},
author = {Vladimir V. Kisil},
journal= {arXiv preprint arXiv:quant-ph/0402035},
year = {2009}
}
Comments
12 pages (AMS-LaTeX); v2: some misprints are corrected; v3: many minor corrections suggested by a referee