dorsal/arxiv
View Schemap-Mechanics and De Donder-Weyl Theory
| Authors | Vladimir V. Kisil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306101 |
| URL | https://arxiv.org/abs/quant-ph/0306101 |
| Journal | Proc. Inst. of Maths of NAS of Ukraine, 50:1108-1115 (2004) |
Abstract
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 operator
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"abstract": "The orbit method of Kirillov is used to derive the p-mechanical brackets\n[quant-ph/0212101]. They generate the quantum (Moyal) and classic (Poisson)\nbrackets on respective orbits corresponding to representations of the\nHeisenberg group. The extension of p-mechanics to field theory is made through\nthe De Donder-Weyl Hamiltonian formulation. The principal step is the\nsubstitution of the Heisenberg group with Galilean. Keywords: Classic and\nquantum mechanics, Moyal brackets, Poisson brackets, commutator, Heisenberg\ngroup, orbit method, deformation quantisation, representation theory, De\nDonder-Weyl field theory, Galilean group, Clifford algebra, conformal M\\\"obius\ntransformation, Dirac operator",
"arxiv_id": "quant-ph/0306101",
"authors": [
"Vladimir V. Kisil"
],
"categories": [
"quant-ph"
],
"journal_ref": "Proc. Inst. of Maths of NAS of Ukraine, 50:1108-1115 (2004)",
"title": "p-Mechanics and De Donder-Weyl Theory",
"url": "https://arxiv.org/abs/quant-ph/0306101"
},
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