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Wigner–Weyl isomorphism for quantum mechanics on Lie groups

Mukunda, N and Marmo, G and Zampini, A and Chaturvedi, S and Simon, R (2005) Wigner–Weyl isomorphism for quantum mechanics on Lie groups. In: Journal of Mathematical Physics, 46 (1). 012106/1-21.


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The Wigner–Weyl isomorphism for quantum mechanics on a compact simple Lie group G is developed in detail. Several features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion of a semiquantized phase space, a structure on which the Weyl symbols of operators turn out to be naturally defined and, figuratively speaking, located midway between the classical phase space T*G and the Hilbert space of square integrable functions on G. General expressions for the star product for Weyl symbols are presented and explicitly worked out for the angle-angular momentum case.

Item Type: Journal Article
Publication: Journal of Mathematical Physics
Publisher: American Institute of Physics
Additional Information: Copyright for this article belongs to American Institute of Physics (AIP).
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Date Deposited: 08 Feb 2005
Last Modified: 04 Jan 2013 06:58
URI: http://eprints.iisc.ac.in/id/eprint/2755

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