Geodesic
Adiabatic Limit for Some Nonlinear Equations of Gauge Field Theory
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 3, Tome 3 (2003), pp. 33-42 
A. G. Sergeev. Adiabatic Limit for Some Nonlinear Equations of Gauge Field Theory. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 3, Tome 3 (2003), pp. 33-42. http://geodesic.mathdoc.fr/item/CMFD_2003_3_a1/
@article{CMFD_2003_3_a1,
     author = {A. G. Sergeev},
     title = {Adiabatic {Limit} for {Some} {Nonlinear} {Equations} of {Gauge} {Field} {Theory}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {33--42},
     year = {2003},
     volume = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2003_3_a1/}
}
TY  - JOUR
AU  - A. G. Sergeev
TI  - Adiabatic Limit for Some Nonlinear Equations of Gauge Field Theory
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2003
SP  - 33
EP  - 42
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/CMFD_2003_3_a1/
LA  - ru
ID  - CMFD_2003_3_a1
ER  - 
%0 Journal Article
%A A. G. Sergeev
%T Adiabatic Limit for Some Nonlinear Equations of Gauge Field Theory
%J Contemporary Mathematics. Fundamental Directions
%D 2003
%P 33-42
%V 3
%U http://geodesic.mathdoc.fr/item/CMFD_2003_3_a1/
%G ru
%F CMFD_2003_3_a1

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider the adiabatic limit for nonlinear dynamic equations of gauge field theory. Our main example of such equations is given by the Abelian $(2+1)$-dimensional Higgs model. We show next that the Taubes correspondence, which assigns pseudoholomorphic curves to solutions of Seiberg–Witten equations on symplectic 4-manifolds, may be interpreted as a complex analogue of the adiabatic limit construction in the $(2+1)$-dimensional case.

[S-Che] Sergeev A. G., Chechin S. V., “O rasseyanii medlenno dvizhuschikhsya vikhrei v abelevoi $(2+1)$-mernoi modeli Khiggsa”, Teor. i mat. fiz., 85 (1990), 397–411 | MR

[J-T] Jaffe A., Taubes C. H., Vortices and monopoles, Birkhäuser, Boston, 1980 | MR | Zbl

[Ma] Manton N. S., “A remark on the scattering of BPS monopoles”, Phys. Lett. B, 110 (1982), 54–56 | DOI | MR | Zbl

[Stu1] Stuart D., “Dynamics of Abelian Higgs vortices in the near Bogomolny regime”, Commun. Math. Phys., 159 (1994), 51–91 | DOI | MR | Zbl

[Stu2] Stuart D., “Periodic solutions of the Abelian Higgs model and rigid rotation of vortices”, Geom. Funct. Anal., 9 (1999), 568–595 | DOI | MR | Zbl

[T1] Taubes C. H., “SW $\Rightarrow$ Gr: From the Seiberg–Witten equations to pseudo-holomorphic curves”, J. Am. Math. Soc., 9 (1996), 845–918 | DOI | MR | Zbl

[T2] Taubes C. H., “Gr $\Rightarrow$ SW: From pseudo-holomorphic curves to Seiberg–Witten solutions”, J. Differ. Geom., 51 (1999), 203–334 | MR | Zbl