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The Schwinger Representation of a Group: Concept and Applications

Chaturvedi, S and Marmo, G and Mukunda, N (2006) The Schwinger Representation of a Group: Concept and Applications. In: Reviews in Mathematical Physics (RMP), 18 (8). pp. 887-912.

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The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for SU(2), SO(3) and SU(n) for all n are constructed via specific carrier spaces and group actions. In the SU(2) case connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.

Item Type: Journal Article
Publication: Reviews in Mathematical Physics (RMP)
Publisher: World Scientific
Additional Information: Copyright of this article belongs to World Scientific.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 14 May 2008
Last Modified: 19 Sep 2010 04:44
URI: http://eprints.iisc.ac.in/id/eprint/13976

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