p-Mechanics and Field Theory

Details p-Mechanics and Field Theory p-Mechanics and Field Theory

2004-02-04

arxiv.org/abs/quant-ph/0402035v3

Rept.Math.Phys. 56 (2005) 161-174

Physics

Quantum Physics

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

Scientific paper

10.1016/S0034-4877(05)80068-0

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.

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