Abstract
Recently, Y. Nambu stated the principles of a new analytical mechanics which allows an odd, as well as an even, number of phase space variables. In this paper we investigate if this mechanics is independent for the odd case of Dirac's classical mechanics because there are reasons which allow one to suspect that independence fails. We prove that Nambu's mechanics is independent of Dirac's mechanics, at least for the odd cases, so that the Nambu mechanics can, in principle, describe physical systems for which the Dirac mechanics is not suitable.
As regards the even case, it is natural to confront the Nambu mechanics with the Hamiltonian one, because both have the same dimension for their phase spaces. In this paper we restrict our study to the comparison of the canonical groups of both formalisms and prove that both groups are different.
García Sucre and Kálnay have suggested that perhaps the Nambu mechanics is the natural one for quarks. We end our study with a brief discussion on this subject whose conclusion seems to support their conjecture.
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Cohen, I., Kálnay, A.J. On Nambu's generalized hamiltonian mechanics. Int J Theor Phys 12, 61–67 (1975). https://doi.org/10.1007/BF01884111
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DOI: https://doi.org/10.1007/BF01884111