A quantum-classical bracket from p-mechanicsV. V. Kisil
School of Mathematics, University of Leeds - Leeds LS2 9JT, UK
received 24 June 2005; accepted in final form 14 October 2005
published online 9 November 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 p-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.
03.65.Sq - Semiclassical theories and applications.
03.65.Db - Functional analytical methods.
03.65.Fd - Algebraic methods.
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