Is Nambu mechanics a generalization of Hamiltonian mechanics?

CDSNS Colloquium
Friday, November 3, 2023 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 249
Cristel Chandre – Georgia Tech – chandre@gatech.edu
Keagan Callis

In 1973, Nambu published an article entitled "Generalized Hamiltonian dynamics". For that purpose, he constructed multilinear brackets - equivalent to Poisson brackets - with some interesting properties reminiscent of the Jacobi identity.
These brackets found some applications in fluid mechanics, plasma physics and mathematical physics with superintegrable systems.

In this seminar, I will recall some basic elements on Nambu mechanics in finite dimension with an n-linear Nambu bracket in dimension larger than n. I will discuss all possible Nambu brackets and compare them with all possible Poisson brackets. I will conclude that Nambu mechanics can hardly be considered a generalization of Hamiltonian mechanics.