13 citations · 13 across the 1 of their papers we have counts for
6 papers · 1 filter
Moyal Deformation, Seiberg-Witten-Map, and Integrable Models
Aristophanes Dimakis, Folkert Muller-Hoissen
A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of function…
Noncommutative Korteweg-de-Vries Equation
Aristophanes Dimakis, Folkert Muller-Hoissen
We construct a deformation quantized version (ncKdV) of the KdV equation which possesses an infinite set of conserved densities. Solutions of the ncKdV are obtained from solutions…
A Noncommutative Version of the Nonlinear Schrodinger Equation
Aristophanes Dimakis, Folkert Muller-Hoissen
We apply a (Moyal) deformation quantization to a bicomplex associated with the classical nonlinear Schrodinger equation. This induces a deformation of the latter equation to noncom…
Noncommutative Geometry and Integrable Models
A. Dimakis, F. Mueller-Hoissen
A construction of conservation laws for -models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing t…
Noncommutative Differential Calculus: Quantum Groups, Stochastic Processes, and the Antibracket
A. Dimakis, F. M"uller-Hoissen
We explore a differential calculus on the algebra of smooth functions on a manifold. The former is `noncommutative' in the sense that functions and differentials do not commute, in…
Differential Calculus and Discrete Structures
A. Dimakis, F. M"uller-Hoissen
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall s…