Communications in Mathematical Physics

, Volume 17, Issue 3, pp 210–232 | Cite as

Derivations of Lie brackets and canonical quantisation

  • A. Joseph


An extensive analysis of the Dirac problem of canonical quantisation is reported. In this a known solution [1] has been found to be unique to within a canonical transformation under a certain prescribed condition. This proves a conjecture due to Streater [2]. A further canonically inequivalent solution is obtained by relaxing this condition. The results obtained are discussed in terms of the derivation algebras pertaining to the Classical and Quantum Lie brackets. Applications to the study of higher symmetries and to realisations of Lie algebras as polynomial functions of canonical operators are pointed out.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Polynomial Function 
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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • A. Joseph
    • 1
    • 2
  1. 1.Mathematical InstituteOxford
  2. 2.Physics DepartmentTel-Aviv UniversityTel-AvivIsrael

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