# nLab Nambu mechanics

Contents

### Context

#### Higher symplectic geometry

symplectic geometry

higher symplectic geometry

## Classical mechanics and quantization

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 18:09:12. See the history of this page for a list of all contributions to it.