Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence of Projections as Gauge Equivalence on Noncommutative Space   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
$\R^4$.

4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th