Is Nambu mechanics a generalization of Hamiltonian mechanics?
Cristel Chandre
I2M
https://sites.google.com/view/cchandre
Date(s) : 03/10/2024 iCal
11h00 - 12h00
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.
Reference: C. Chandre and A. Horikoshi, Classical Nambu brackets in higher dimensions, J. Math. Phys. 64, 052702 (2023)
Catégories
