under construction
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).
One example that naturally gives rise to Nambu mechanics is the relativistic membrane, see at membrane matrix model and at BLG model.
Nambu mechanics and Nambu brackets were introduced in
Detailed analysis is in
Tamiaki Yoneya, Generalized Hamilton-Jacobi theory of Nambu Mechanics (arXiv:1612.08509)
Tamiaki Yoneya, Lectures on Higher-Gauge Symmetries from Nambu Brackets and Covariantized M(atrix) Theory, lectures delivered in the workshop “Higher Structure in String Theory and M-theory”, TFC Thematic Program, Fundamental Problems on Quantum Physics, Tohoku University (March 7-11, 2016), (arXiv:1612.08513)
Review:
Thomas L. Curtright, Cosmas K. Zachos, Classical and Quantum Nambu Mechanics, Phys. Rev. D 68 085001 (2003) [arXiv:hep-th/0212267, doi:10.1103/PhysRevD.68.085001]
Wikipedia, Nambu mechanics
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 7, 2023 at 17:06:05. See the history of this page for a list of all contributions to it.