133 research outputs found
A Quantum-Classical Brackets from p-Mechanics
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
mixingComment: LaTeX, 7 pages (EPL style), no figures; v2: example of dynamics with
two different Planck's constants is added, minor corrections; v3: major
revion, a complete example of quantum-classic dynamics is given; v4: few
grammatic correction
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