Equivalence of Projections as Gauge Equivalence on Noncommutative Space

Details Equivalence of Projections as Gauge Equivalence on Noncommutative Space Equivalence of Projections as Gauge Equivalence on Noncommutative Space

2000-05-22

arxiv.org/abs/hep-th/0005199v2

Commun.Math.Phys. 217 (2001) 579-593

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, AMSLaTeX, v2: refined explanations, typos corrected

Scientific paper

10.1007/PL00005554

Projections play crucial roles in the ADHM construction on noncommutative $\R^4$. In this article a framework for the description of equivalence relations between projections is proposed. We treat the equivalence of projections as ``gauge equivalence'' on noncommutative space. We find an interesting application of this framework to the study of U(2) instanton on noncommutative $\R^4$: A zero winding number configuration with a hole at the origin is ``gauge equivalent'' to the noncommutative analog of the BPST instanton. Thus the ``gauge transformation'' in this case can be understood as a noncommutative resolution of the singular gauge transformation in ordinary $\R^4$.

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