Realizations of Lie Algebras Through Rational Functions of Canonical Variables

  • H. D. Doebner
  • T. D. Palev
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 7/1970)


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 .


Steklov Institute Canonical Variable Trace Formula Division Ring Group Theoretical Approach 


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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • H. D. Doebner
    • 1
    • 2
  • T. D. Palev
    • 3
  1. 1.Institute for Theoretical Physics (I)University of MarburgFed. Rep. Germany
  2. 2.Institute for Theoretical PhysicsTechnical University of ClausthalFed. Rep. Germany
  3. 3.Institute for PhysicsBulgarian Academy of SciencesSofiaBulgaria

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