p-Mechanics and field theory

The orbit method of Kirillov is used to derive the p-mechanical brackets [25]. They generate the quantum (Moyal) and classical (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.