Classical and quantum Kummer shape algebras

Abstract

We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, is also presented.

arXiv comment39 pages, 2 figures

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• Some aspects of positive kernel method of quantization