Theoretical and Mathematical Physics

, Volume 95, Issue 1, pp 367–377 | Cite as

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

  • V. P. Karasev


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.


Physic Problem Frequency Conversion Dynamical Symmetry Multiphoton Process Polynomial Deformation 
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© Plenum Publishing Corporation 1993

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  • V. P. Karasev

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