A Formula for the Local Solution of the SelfDual YangMills Equations
Abstract
Twistor techniques are used to give all local solutions to the selfdual YangMills equations for any matrix gauge group. The field is expressed in terms of an infinite sum, which is a contour integral analogue of a pathordered exponential integral, over the twistor datum. The key step is the solution of the matrixvalued CousinHilbertRiemann problem on the sphere, that is, of trivializing a holomorphic vector bundle given by a transition function over an annulus.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 November 1987
 DOI:
 10.1098/rspa.1987.0137
 Bibcode:
 1987RSPSA.414..135H