CONTRACTIONS OF LIE ALGEBRA REPRESENTATIONS

Author:

CATTANEO U.1,WRESZINSKI W. F.2

Affiliation:

1. CERFIM, Via F. Rusca 1, CH-6601 Locarno, Switzerland

2. Instituto de Física, Universidade de São Paulo, C. P. 66318, 05389-970 São Paulo, SP, Brazil

Abstract

A theory of contractions of Lie algebra representations on complex Hilbert spaces is proposed, based on Trotter's theory of approximating sequences of Banach spaces. Its main distinguishing feature is a careful definition of the carrier space of the limit Lie algebra representation. A set of quite general conditions on the contracting representations, satisfied in all known examples, is proven to be sufficient for the existence of such a representation. In order to show how natural the suggested framework is, the general theory is applied to the contraction of [Formula: see text] into the Lie algebra [Formula: see text] of the 3-dimensional Heisenberg group and to the related study of the limit N→∞ of a quantum system of N identical two-level particles.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

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