nLab Nambu mechanics

Contents

Context

Higher symplectic geometry

under construction

Contents

Idea

What is called Nambu mechanics is a generalization of the formulation of classical mechanics (prequantum geometry) via Poisson brackets to bracket-operations of arity $(n+1)$ higher than 2 – the Nambu brackets –, with an “(n+1)-Lie algebra”-structure (see the discussion there for distinction with proper Lie n-algebras).

Examples

The membrane

One example that naturally gives rise to Nambu mechanics is the relativistic membrane, see at membrane matrix model and at BLG model.

References

General

Nambu mechanics and Nambu brackets were introduced in

Detailed analysis is in

Reviews include

Interpretation in higher symplectic geometry

Comments on interpreting Nambu mechanics in 2-plectic geometry (and in view of the IKKT matrix model) appear in

For background on this see also the discussion at 3-Lie algebra on how these are given by Lie 2-algebras (as metric Lie 2-algebras)

Last revised on December 28, 2016 at 13:09:12. See the history of this page for a list of all contributions to it.