Wigner distributions and quantum mechanics on Lie groups: The case of the regular representation

Mukunda, N and Arvind, * and Chaturvedi, S and Simon, R (2004) Wigner distributions and quantum mechanics on Lie groups: The case of the regular representation. In: Journal of Mathematical Physics, 45 (1). pp. 114-148.

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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 R n 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:	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:	03 Nov 2004
Last Modified:	19 Sep 2010 04:17
URI:	http://eprints.iisc.ac.in/id/eprint/2240

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