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Contemporary Mathematics. Fundamental Directions, 2003, Volume 3, Pages 33–42 (Mi cmfd14)  
Adiabatic Limit for Some Nonlinear Equations of Gauge Field Theory

A. G. Sergeev

Steklov Mathematical Institute, Russian Academy of Sciences
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Abstract: 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.
English version:
Journal of Mathematical Sciences, 2004, Volume 124, Issue 6, Pages 5407–5416
DOI: https://doi.org/10.1023/B:JOTH.0000047361.38336.26
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: A. G. Sergeev, “Adiabatic Limit for Some Nonlinear Equations of Gauge Field Theory”, 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, CMFD, 3, MAI, M., 2003, 33–42; Journal of Mathematical Sciences, 124:6 (2004), 5407–5416
Citation in format AMSBIB
\Bibitem{Ser03}
\by A.~G.~Sergeev
\paper Adiabatic Limit for Some Nonlinear Equations of Gauge Field Theory
\inbook 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
\serial CMFD
\yr 2003
\vol 3
\pages 33--42
\publ MAI
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd14}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2129143}
\zmath{https://zbmath.org/?q=an:1072.58007}
\transl
\jour Journal of Mathematical Sciences
\yr 2004
\vol 124
\issue 6
\pages 5407--5416
\crossref{https://doi.org/10.1023/B:JOTH.0000047361.38336.26}
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