2005/06/30 by Vladimir V. Kisil · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Mechanics and Applications #Topological and Geometric Data Analysis #advanced mathematical theories #quant-ph
paper · pdf · doi:10.1209/epl/i2005-10324-7
published as Europhys. Lett., 72 (6), pp. 873-?879 (2005) · 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 corrections
arxiv created 2005/11/04 · openalex publication_date 2005/11/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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.