The Schwinger representation of a group: concept and applications

Chaturvedi, S. ; Marmo, G. ; Mukunda, N. ; Simon, R. ; Zampini, A. (2006) The Schwinger representation of a group: concept and applications Reviews in Mathematical Physics, 18 (8). pp. 887-912. ISSN 0129-055X

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Official URL: http://www.worldscinet.com/rmp/18/1808/S0129055X06...

Related URL: http://dx.doi.org/10.1142/S0129055X06002802

Abstract

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:Article
Source:Copyright of this article belongs to World Scientific Publishing Company.
Keywords:Schwinger Representation; Schwinger Oscillator Construction; Compact Semi-simple Lie Groups; Majorana Representation for Spin; Wigner Distribution; Wigner-Weyl Isomorphism
ID Code:78459
Deposited On:20 Jan 2012 04:16
Last Modified:20 Jan 2012 04:16

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