Volume 72, Number 6, December 2005
|873 - 879
|09 November 2005
A quantum-classical bracket from p-mechanics
School of Mathematics, University of Leeds - Leeds LS2 9JT, UK
Accepted: 14 October 2005
We provide an answer to the long-standing problem of mixing quantum and classical dynamics within a single formalism. The construction is based on -mechanical derivation 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.
PACS: 03.65.Sq – Semiclassical theories and applications / 03.65.Db – Functional analytical methods / 03.65.Fd – Algebraic methods
© EDP Sciences, 2005
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