Topological Charge of U(1) Instantons

Details Topological Charge of U(1) Instantons Topological Charge of U(1) Instantons

2000-10-02

arxiv.org/abs/hep-th/0010006v1

Prog.Theor.Phys.Suppl.144:79-91,2001

Physics

High Energy Physics

High Energy Physics - Theory

49 pages, 7 figures, based on talk given at APCTP-Yonsei Workshop on Noncommutative Field Theories

Scientific paper

10.1143/PTPS.144.79

Non-singular instantons are shown to exist on noncommutative R^4 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 R^4 and the projection operators acting on the representation space of the noncommutative coordinates is reviewed. The integer number of instantons on the noncommutative R^4 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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