title:  Approaches to the quantization of Nambu mechanics and Nambu brackets

abstract: The Nambu mechanics was first proposed by Y. Nambu in 1973 as a
possible generalization of Hamiltonian dynamics. The proposal consisted of
extending the usual phase space of even dimensions to three (and arbitrary) dimensions,
in such a way that two (and more) Hamiltonians play symmetrical roles.
The problem of quantization of this system has been still to be solved.
We give an overview on the status of this largely unfamiliar direction from an aspect of
the generalized Hamilton-Jacobi formalism and its possible relevance to quantization.