Generalized Abelian Deformations: Application to Nambu Mechanics

Abstract

We study Abelian generalized deformations of the usual product of polynomials introduced in an earlier work. We construct an explicit example for the case of \(\mathfrak{s}\mathfrak{u} \)(2) which provides a tentative quantum-mechanical description of Nambu mechanics on \(\mathbb{R}^3 \). By introducing the notions of strong and weak triviality of generalized deformations, we show that the Zariski product is never trivial in either sense, while the example constructed here in a quantum-mechanical context is strongly nontrivial.