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.Comment: 12 pages (AMS-LaTeX); v2: some misprints are corrected; v3: many
minor corrections suggested by a refere
