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 operatorComment: LaTeX, 8 pages, no figure
