Topological Charge of U(1) Instantons
Abstract
Non-singular instantons are shown to exist on noncommutative R4 even with a U(1) gauge group. Their existence is primarily due to the noncommutativity of the space. The relation between U(1) instantons on noncommutative R4 and the projection operators acting on the representation space of the noncommutative coordinates is reviewed. The integer number of instantons on the noncommutative R4 can be understood as the winding number of the U(1) gauge field as well as the dimension of the projection on the representation space.
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