Nambu bracket and M-theory

Abstract

Nambu proposed an extension of dynamical system through the introduction of a new bracket (Nambu bracket) in 1973. This article is a short review of the developments after his paper. Some emphasis are put on a viewpoint that the Nambu bracket naturally describes extended objects which appear in M-theory and the fluid dynamics. The latter part of the paper is devoted to a review of the studies on the Nambu bracket (Lie 3-algebra) in Bagger-Lambert-Gustavsson theory of multiple M2-branes. This paper is a contribution to the proceedings of Nambu memorial symposium (Osaka City University, September 29, 2015).

25 pages, contribution to the proceedings of Nambu memorial symposium, Osaka City University, September 29, 2015, v2 minor modifications

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Cited by in corpus (16)

• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Nambu bracket and M-theory
• Higher (Odd) Dimensional Quantum Hall Effect and Extended Dimensional Hierarchy
• Generalized Hamilton-Jacobi theory of Nambu Mechanics
• Interference and Oscillation in Nambu Quantum Mechanics
• Classification of the classical $SL(2,\mathbb{R})$ gauge transformations in the rigid body
• Integrability structures in string theory
• Hidden Nambu mechanics II: Quantum/semiclassical dynamics
• Generalization of Hamiltonian Mechanics to a Three Dimensional Phase Space
• Quantization of Nambu Brackets from Operator Formalism in Classical Mechanics
• A group action principle for Nambu dynamics of spin degrees of freedom
• Generalizing Hamiltonian Mechanics with Closed Differential Forms
• Deformation of Matrix Geometry via Landau Level Evolution
• Shadow Hamiltonians of structure-preserving integrators for Nambu mechanics
• Nambu dynamics and its noncanonical Hamiltonian representation in many degrees of freedom systems
• Generalized Heisenberg Dynamics Revisited