Equivalence of Projections as Gauge Equivalence on Noncommutative Space

Abstract

Projections play crucial roles in the ADHM construction on noncommutative ${\mathbb{R}}^4$. 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 ${\mathbb{R}}^4$: 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 ${\mathbb{R}}^4$.

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

References in corpus (3)

• Instantons on Noncommutative R^4 and Projection Operators
• Space-Time Foam From Non-Commutative Instantons
• Twisted Bundle on Noncommutative Space and U(1) Instanton

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