Recent Developments in Instantons in Noncommutative ℝ𝟒
We review recent developments in noncommutative deformations of instantons in ℝ4. In the operator formalism, we study how to make noncommutative instantons by using the ADHM method, and we review the relation between topological charges and noncommutativity. In the ADHM methods, there exist instanto...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2010/270694 |
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| _version_ | 1832560198208716800 |
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| author | Akifumi Sako |
| author_facet | Akifumi Sako |
| author_sort | Akifumi Sako |
| collection | DOAJ |
| description | We review recent developments in noncommutative deformations of instantons
in ℝ4. In the operator formalism, we study how to make noncommutative instantons
by using the ADHM method, and we review the relation between topological
charges and noncommutativity. In the ADHM methods, there exist instantons
whose commutative limits are singular. We review smooth noncommutative deformations
of instantons, spinor zero-modes, the Green's functions, and the ADHM
constructions from commutative ones that have no singularities. It is found that
the instanton charges of these noncommutative instanton solutions coincide with the
instanton charges of commutative instantons before noncommutative deformation.
These smooth deformations are the latest developments in noncommutative gauge
theories, and we can extend the procedure to other types of solitons. As an example,
vortex deformations are studied. |
| format | Article |
| id | doaj-art-9c457edaaa024ed0a01191760c4f50fc |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9c457edaaa024ed0a01191760c4f50fc2025-02-03T01:28:11ZengWileyAdvances in Mathematical Physics1687-91201687-91392010-01-01201010.1155/2010/270694270694Recent Developments in Instantons in Noncommutative ℝ𝟒Akifumi Sako0Department of General Education, Kushiro National College of Technology Otanoshike-Nishi 2-32-1, Kushiro 084-0916, JapanWe review recent developments in noncommutative deformations of instantons in ℝ4. In the operator formalism, we study how to make noncommutative instantons by using the ADHM method, and we review the relation between topological charges and noncommutativity. In the ADHM methods, there exist instantons whose commutative limits are singular. We review smooth noncommutative deformations of instantons, spinor zero-modes, the Green's functions, and the ADHM constructions from commutative ones that have no singularities. It is found that the instanton charges of these noncommutative instanton solutions coincide with the instanton charges of commutative instantons before noncommutative deformation. These smooth deformations are the latest developments in noncommutative gauge theories, and we can extend the procedure to other types of solitons. As an example, vortex deformations are studied.http://dx.doi.org/10.1155/2010/270694 |
| spellingShingle | Akifumi Sako Recent Developments in Instantons in Noncommutative ℝ𝟒 Advances in Mathematical Physics |
| title | Recent Developments in Instantons in Noncommutative ℝ𝟒 |
| title_full | Recent Developments in Instantons in Noncommutative ℝ𝟒 |
| title_fullStr | Recent Developments in Instantons in Noncommutative ℝ𝟒 |
| title_full_unstemmed | Recent Developments in Instantons in Noncommutative ℝ𝟒 |
| title_short | Recent Developments in Instantons in Noncommutative ℝ𝟒 |
| title_sort | recent developments in instantons in noncommutative r𝟒 |
| url | http://dx.doi.org/10.1155/2010/270694 |
| work_keys_str_mv | AT akifumisako recentdevelopmentsininstantonsinnoncommutativer4 |