Comments on the U (2) noncommutative instanton

We discuss the 't Hoof ansatz for instanton solutions in noncommutative U(2 ) Yang-Mills theory. We show that the extension of the ansatz leading to si ngular solutions in the commutative case, yields to non self-dual (or self- antidual) configurations in noncommutative space-time. A proposal leading t o selfdual solutions with Q = 1 topological charge (the equivalent of the r egular BPST ansatz) can be engineered, but in that case the gauge field and the curvature are not Hermitian (although the resulting Lagrangian is real ). (C) 2001 Published by Elsevier Science B.V.