Realizations of Lie Algebras Through Rational Functions of Canonical Variables
The group theoretical approach to relativistic and non-relativistic quantum mechanics is usually based on integrable representations of Lie-algebras G being consid- ered as dynamical algebras, non-invariance algebras or spectrum-generating algebras. Because the generators of G are, in general,physical observables, it is reasonable to assume that they can be expressed as functions of creation and annihilation operators Ai, A i * or of momentum and position operators Pi, Qi, i=l,...,n . If such functions exist for a given algebra G , we call this a canonical realization of G .
KeywordsSteklov Institute Canonical Variable Trace Formula Division Ring Group Theoretical Approach
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