Moyal Nahm Equations

Abstract

Various aspects of the Nahm equations in 3 and 7 dimensions are investigated. The residues of the variables at simple poles in the 7-dimensional case form an algebra. A large class of matrix representations of this algebra is constructed. The large $N$ limit of these equations is taken by replacing the commutators by Moyal Brackets, and a set of non trivial solutions in a generalised form of Wigner distribution functions is obtained.

15 pages, latex, no figures

References in corpus (5)

• Matrix String Theory
• Higher Dimensional Analogues of Donaldson-Witten Theory
• Integrable Symplectic Trilinear Interaction Terms for Matrix Membranes
• Moyal Brackets in M-Theory
• Moyal Brackets, Star Products and the Generalised Wigner Function

Cited by in corpus (12)

• Anti-self-dual Yang-Mills equations on noncommutative spacetime
• Admissible states in quantum phase space
• Formal solutions of stargenvalue equations
• Enhancons, Fuzzy Spheres and Multi-Monopoles
• Calibrations, Monopoles and Fuzzy Funnels
• Generalized Weyl-Wigner map and Vey quantum mechanics
• Time dependent transformations in deformation quantization
• Gauge theories and non-commutative geometry
• Nahm equations in supersymmetric mechanics
• On the Moyal deformation of Nahm Equations in seven dimensions
• Gauge Theories and Non-Commutative Geometry
• Stargenfunctions, generally parametrized systems and a causal formulation of phase space quantum mechanics