Coherent States on Lie Algebras: A Constructive Approach

Details Coherent States on Lie Algebras: A Constructive Approach Coherent States on Lie Algebras: A Constructive Approach

1997-10-23

arxiv.org/abs/physics/9710032v1

Int.J.Theor.Phys. 38 (1999) 675-700

Physics

Mathematical Physics

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Scientific paper

We generalise the notion of coherent states to arbitrary Lie algebras by making an analogy with the GNS construction in $C^*$-algebras. The method is illustrated with examples of semisimple and non-semisimple finite dimensional Lie algebras as well as loop and Kac-Moody algebras. A deformed addition on the parameter space is also introduced simplifying some expressions and some applications to conformal field theory is pointed out, e.g. are differential operator and free field realisations found. PACS: 02.20.S, 03.65.F, 11.25.H Keywords: coherent states, Lie and Kac-Moody algebras, realisations.

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