Instanton-anti-instanton solutions of discrete Yang-Mills equations

Volodymyr Sushch

Mathematica Bohemica (2012)

  • Volume: 137, Issue: 2, page 219-228
  • ISSN: 0862-7959

Abstract

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We study a discrete model of the S U ( 2 ) Yang-Mills equations on a combinatorial analog of 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.

How to cite

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Sushch, Volodymyr. "Instanton-anti-instanton solutions of discrete Yang-Mills equations." Mathematica Bohemica 137.2 (2012): 219-228. <http://eudml.org/doc/247079>.

@article{Sushch2012,
abstract = {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.},
author = {Sushch, Volodymyr},
journal = {Mathematica Bohemica},
keywords = {Yang-Mills equations; self-dual equations; anti-self-dual equations; instanton; anti-instanton; difference equations; Yang-Mills equation; self-dual equation; anti-self-dual equation; instanton; anti-instanton; difference equation},
language = {eng},
number = {2},
pages = {219-228},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Instanton-anti-instanton solutions of discrete Yang-Mills equations},
url = {http://eudml.org/doc/247079},
volume = {137},
year = {2012},
}

TY - JOUR
AU - Sushch, Volodymyr
TI - Instanton-anti-instanton solutions of discrete Yang-Mills equations
JO - Mathematica Bohemica
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 137
IS - 2
SP - 219
EP - 228
AB - 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.
LA - eng
KW - Yang-Mills equations; self-dual equations; anti-self-dual equations; instanton; anti-instanton; difference equations; Yang-Mills equation; self-dual equation; anti-self-dual equation; instanton; anti-instanton; difference equation
UR - http://eudml.org/doc/247079
ER -

References

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  1. Atiyah, M. F., Geometry of Yang-Mills Fields, Lezione Fermiane, Scuola Normale Superiore, Pisa (1979). (1979) Zbl0435.58001MR0554924
  2. Dezin, A. A., Multidimensional Analysis and Discrete Models, CRC Press, Boca Raton (1995). (1995) Zbl0851.39008MR1397027
  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. (1993) MR1250743
  4. Freed, D., Uhlenbeck, K., Instantons and Four-Manifolds, Springer, New York (1984). (1984) Zbl0559.57001MR0757358
  5. Nash, C., Sen, S., Topology and Geometry for Physicists, Acad. Press, London (1989). (1989) MR0776042
  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. (1997) Zbl0935.53017MR1620141
  7. Sushch, V., Discrete model of Yang-Mills equations in Minkowski space, Cubo A Math. Journal. 6 (2004), 35-50. (2004) Zbl1081.81082MR2092042
  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. (2006) Zbl1139.81375MR2287294

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