### Abstract

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 the 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}.

Original language | English |
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Pages (from-to) | 579-593 |

Number of pages | 15 |

Journal | Communications in Mathematical Physics |

Volume | 217 |

Issue number | 3 |

Publication status | Published - 03-2001 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Communications in Mathematical Physics*, vol. 217, no. 3, pp. 579-593.

**Equivalence of projections as gauge equivalence on noncommutative space.** / Furuuchi, Kazuyuki.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Equivalence of projections as gauge equivalence on noncommutative space

AU - Furuuchi, Kazuyuki

PY - 2001/3

Y1 - 2001/3

N2 - Projections play crucial roles in the ADHM construction on noncommutative ℝ4. 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 the U(2) instanton on noncommutative ℝ4: 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 ℝ4.

AB - Projections play crucial roles in the ADHM construction on noncommutative ℝ4. 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 the U(2) instanton on noncommutative ℝ4: 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 ℝ4.

UR - http://www.scopus.com/inward/record.url?scp=0035531648&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035531648&partnerID=8YFLogxK

M3 - Article

VL - 217

SP - 579

EP - 593

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -