A group action principle for Nambu dynamics of spin degrees of freedom

TL;DR

This paper develops a group action principle for Nambu dynamics of spin systems, linking classical formulations with quantum transition amplitudes and non-commutative geometry discretizations.

Contribution

It introduces a new group action formulation for Nambu flows that incorporates all defining properties and connects to non-commutative geometry for discretization.

Findings

Consistent description of off-shell states and superpositions in spin dynamics.

Relation between fluctuations of magnetization components.

Link between Nambu mechanics and non-commutative geometry.

Abstract

We describe a formulation of the group action principle, for linear Nambu flows, that explicitly takes into account all the defining properties of Nambu mechanics and illustrate its relevance by showing how it can be used to describe the off-shell states and superpositions thereof that define the transition amplitudes for the quantization of Larmor precession of a magnetic moment. It highlights the relation between the fluctuations of the longitudinal and transverse components of the magnetization. This formulation has been shown to be consistent with the approach that has been developed in the framework of the non commutative geometry of the 3-torus. In this way the latter can be used as a consistent discretization of the former.