Mukunda, N. ; Arvind, ; Chaturvedi, S. ; Simon, R. (2004) Wigner distributions and quantum mechanics on lie groups: the case of the regular representation Journal of Mathematical Physics, 45 (1). pp. 114-148. ISSN 0022-2488
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Official URL: http://jmp.aip.org/resource/1/jmapaq/v45/i1/p114_s...
Related URL: http://dx.doi.org/10.1063/1.1631393
Abstract
We consider the problem of setting up the Wigner distribution for states of a quantum system whose configuration space is a Lie group. The basic properties of Wigner distributions in the familiar Cartesian case are systematically generalized to accommodate new features which arise when the configuration space changes from n-dimensional Euclidean space Rn to a Lie group G. The notion of canonical momentum is carefully analyzed, and the meanings of marginal probability distributions and their recovery from the Wigner distribution are clarified. For the case of compact G an explicit definition of the Wigner distribution is proposed, possessing all the required properties. Geodesic curves in G which help introduce a notion of the midpoint of two group elements play a central role in the construction.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Institute of Physics. |
Keywords: | Wigner Distribution; Quantum Theory; Lie Groups; Probability; Differential Geometry |
ID Code: | 7011 |
Deposited On: | 26 Oct 2010 04:39 |
Last Modified: | 16 May 2016 17:16 |
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