International Journal of Theoretical Physics

, Volume 12, Issue 5, pp 287–292 | Cite as

The Nambu mechanics as a class of singular generalized dynamical formalisms

  • G. J. Ruggeri


In a recent work Nambu has proposed ac-number dynamical formalism which can allow an odd numbern of canonical variables. Naturally associated to this new mechanics there exists ann-linear bracket whose study opens interesting possibilities. The purpose of this work is to show that besides this bracket another one which is bilinear and in fact a Lie bracket can also be associated with the Nambu mechanics. For anyn, however, this bracket is singular. In a sense previously used by the present author, this result exhibits the Nambu mechanics as an interesting class of singular generalized dynamical formalisms irrespective of the number of phase space variables. Reasons are given suggesting that such singular formalisms would be, within our context, the only ones capable of describing classical analogues of generalized quantum systems.


Field Theory Recent Work Phase Space Elementary Particle Quantum Field Theory 
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Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • G. J. Ruggeri
    • 1
  1. 1.Departamento de Física, Facultad de CienciasUniversidad Central de Venezuela and International Centre for Theoretical PhysicsTriesteItaly

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