A Quantum-Classical Brackets from p-Mechanics

Details A Quantum-Classical Brackets from p-Mechanics A Quantum-Classical Brackets from p-Mechanics

2005-06-15

arxiv.org/abs/quant-ph/0506122v4

Europhys. Lett., 72 (6), pp. 873-?879 (2005)

Physics

Quantum Physics

LaTeX, 7 pages (EPL style), no figures; v2: example of dynamics with two different Planck's constants is added, minor correcti

Scientific paper

10.1209/epl/i2005-10324-7

We provide an answer to the long standing problem of mixing quantum and classical dynamics within a single formalism. The construction is based on p-mechanical derivation (quant-ph/0212101, quant-ph/0304023) of quantum and classical dynamics from the representation theory of the Heisenberg group. To achieve a quantum-classical mixing we take the product of two copies of the Heisenberg group which represent two different Planck's constants. In comparison with earlier guesses our answer contains an extra term of analytical nature, which was not obtained before in purely algebraic setup. Keywords: Moyal brackets, Poisson brackets, commutator, Heisenberg group, orbit method, representation theory, Planck's constant, quantum-classical mixing

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