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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  1. H. D. Doebner, T. D. Palev, "The trace formula for canonical realizations of Lie algebras", preprint, University of Marburg, 1970.Google Scholar
  2. H. D. Doebner, T. D. Palev, "On canonical realizations of Lie algebras" (in preparation).Google Scholar
  3. H. D. Doebner, T. D. Palev, "On Lie subalgebras and isomorphisms of the canonical quotient division ring" (in preparation).Google Scholar
  4. T. D. Palev, ICTP Trieste, preprint IC/68/23 (1968).Google Scholar
  5. T. D. Palev, Nuovo Cim. 62, 585 (1969).Google Scholar
  6. H. D. Doebner, B. Pirrung, "On the construction of spectrum-generating algebras by embedding methods", preprint, University of Marburg, 1970.Google Scholar
  7. K. Kademova, T. D. Palev, "Second-order realizations of Lie algebras with parafield operators", preprint, Bulgarian Academy of Sciences, 1970.Google Scholar
  8. K. Kademova, ICTP Trieste, preprint, IC/69/108 (1969) (to appear in Nuclear Physics).Google Scholar
  9. N. Miller, "Lie Theory and Special Functions" (Academic Press,New York 1968). N. Miller, "On Lie Theory and some Special Functions in Mathematical Physics" (American Mathematical Society, Providence, R.I. 1964).Google Scholar
  10. N. Jacobson, “Lecture on Abstract Algebra, I” (Van Nostrand, Princeton 1951). N. Jacobson, “Structure of Rings” (American Mathematical Society, PrOVidence, R.I. 1964).Google Scholar
  11. I. M. Gel‘fand, A. A. Kirillov, “On the division rings connected with enveloping algebras of Lie algebras”, preprint, Steklov Institute of Mathematics, Moscow (1965).Google Scholar
  12. S. Helgason, “Differential Geometry and Symmetric Spaces” (Academic Press, New York 1962).Google Scholar

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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