Polynomial deformations of the Lie algebrasl(2) in problems of quantum optics

Abstract

It is shown that specific (polynomial) deformations of Lie algebras arise naturally as dynamical symmetry algebrasgds of second-quantized models with nonquadratic HamiltoniansH invariant with respect to certain groupsGinv(H). Such deformationssld(2) of the Lie algebrasl(2) are found in a number of models of quantum optics (multiphoton processes, generalized Dicke model, and frequency conversion), and ways to apply thesl(2) formalism to the solution of physics problems are indicated.