THE ADHM CONSTRUCTION OF INSTANTONS ON NONCOMMUTATIVE SPACES

摘要

We present an account of the ADHM construction of instantons on Euclidean space-timenR4 from the point of view of noncommutative geometry. We recall the main ingredientsnof the classical construction in a coordinate algebra format, which we then deform usingna cocycle twisting procedure to obtain a method for constructing families of instantonsnon noncommutative space-time, parametrized by solutions to an appropriate set ofnADHM equations. We illustrate the noncommutative construction in two special cases:nthe Moyal–Groenewold plane R4nu0001 and the Connes–Landi plane R4θ.