| Title:
|
Instanton-anti-instanton solutions of discrete Yang-Mills equations (English) |
| Author:
|
Sushch, Volodymyr |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
137 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
219-228 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study a discrete model of the $SU(2)$ Yang-Mills equations on a combinatorial analog of $\mathbb {R}^4$. Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both the techniques of a double complex and the quaternionic approach. (English) |
| Keyword:
|
Yang-Mills equations |
| Keyword:
|
self-dual equations |
| Keyword:
|
anti-self-dual equations |
| Keyword:
|
instanton |
| Keyword:
|
anti-instanton |
| Keyword:
|
difference equations |
| MSC:
|
39A12 |
| MSC:
|
81T13 |
| MSC:
|
81T25 |
| idZBL:
|
Zbl 1265.39010 |
| idMR:
|
MR2978267 |
| DOI:
|
10.21136/MB.2012.142867 |
| . |
| Date available:
|
2012-06-08T10:14:50Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142867 |
| . |
| Reference:
|
[1] Atiyah, M. F.: Geometry of Yang-Mills Fields.Lezione Fermiane, Scuola Normale Superiore, Pisa (1979). Zbl 0435.58001, MR 0554924 |
| Reference:
|
[2] Dezin, A. A.: Multidimensional Analysis and Discrete Models.CRC Press, Boca Raton (1995). Zbl 0851.39008, MR 1397027 |
| Reference:
|
[3] Dezin, A. A.: Models generated by the Yang-Mills equations.Differ. Uravn. 29 (1993), 846-851; English translation in Differ. Equ. 29 (1993), 724-728. MR 1250743 |
| Reference:
|
[4] Freed, D., Uhlenbeck, K.: Instantons and Four-Manifolds.Springer, New York (1984). Zbl 0559.57001, MR 0757358 |
| Reference:
|
[5] Nash, C., Sen, S.: Topology and Geometry for Physicists.Acad. Press, London (1989). MR 0776042 |
| Reference:
|
[6] Sushch, V.: Gauge-invariant discrete models of Yang-Mills equations.Mat. Zametki. 61 (1997), 742-754; English translation in Math. Notes. 61 (1997), 621-631. Zbl 0935.53017, MR 1620141 |
| Reference:
|
[7] Sushch, V.: Discrete model of Yang-Mills equations in Minkowski space.Cubo A Math. Journal. 6 (2004), 35-50. Zbl 1081.81082, MR 2092042 |
| Reference:
|
[8] Sushch, V.: A gauge-invariant discrete analog of the Yang-Mills equations on a double complex.Cubo A Math. Journal. 8 (2006), 61-78. Zbl 1139.81375, MR 2287294 |
| . |
