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Article Dans Une Revue Journal of Mathematical Physics Année : 2023

Classical Nambu brackets in higher dimensions

Atsushi Horikoshi
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Résumé

We consider n-linear Nambu brackets in dimension N higher than n. Starting from a Hamiltonian system with a Poisson bracket and K Casimir invariants defined in the phase space of dimension N = K+2M, where M is the number of effective degrees of freedom, we investigate a necessary and sufficient condition for this system to possess n-linear Nambu brackets. For the case of n = 3, by looking for the possible solutions to the fundamental identity, the condition is found to be N = K+2, i.e., the system should have effectively one degree of freedom. Locally, it is shown that there is only one fundamental solution, up to a local change of variables, and this solution is the canonical Nambu bracket, generated by Levi-Civita tensors. These results generalize to the case of n(≥ 4)-linear Nambu brackets.
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Dates et versions

hal-03356663 , version 1 (28-09-2021)

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Cristel Chandre, Atsushi Horikoshi. Classical Nambu brackets in higher dimensions. Journal of Mathematical Physics, 2023, 64, pp.052702. ⟨10.1063/5.0073169⟩. ⟨hal-03356663⟩
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