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Tr. Mosk. Mat. Obs., 2011, Volume 72, Issue 2, Pages 281–314 (Mi mmo19)  

This article is cited in 8 scientific papers (total in 8 papers)

Justification of the adiabatic principle in the Abelian Higgs model

R. V. Palvelev

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: A justification of the adiabatic principle for the $(2+1)$-dimensional Abelian Higgs model is given. It is shown that near any geodesic on the space of static solutions there exists a solution of the dynamical Euler-Lagrange equations.

Key words and phrases: Abelian Higgs model of field theory, Manton approximation, adiabatic limit, scattering of vortices.

Full text: PDF file (334 kB)
References: PDF file   HTML file

English version:
Transactions of the Moscow Mathematical Society, 2011, 72, 219–244

Bibliographic databases:

UDC: 517.956.35+517.958
MSC: 35Q60, 81T40, 53P99
Received: 11.04.2011

Citation: R. V. Palvelev, “Justification of the adiabatic principle in the Abelian Higgs model”, Tr. Mosk. Mat. Obs., 72, no. 2, MCCME, Moscow, 2011, 281–314; Trans. Moscow Math. Soc., 72 (2011), 219–244

Citation in format AMSBIB
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\by R.~V.~Palvelev
\paper Justification of the adiabatic principle in the Abelian Higgs model
\serial Tr. Mosk. Mat. Obs.
\yr 2011
\vol 72
\issue 2
\pages 281--314
\publ MCCME
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/mmo19}
\zmath{https://zbmath.org/?q=an:06026279}
\elib{http://elibrary.ru/item.asp?id=21369345}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2011
\vol 72
\pages 219--244
\crossref{https://doi.org/10.1090/S0077-1554-2012-00189-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84904047441}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. V. Palvelev, A. G. Sergeev, “Justification of the adiabatic principle for hyperbolic Ginzburg–Landau equations”, Proc. Steklov Inst. Math., 277 (2012), 191–205  mathnet  crossref  mathscinet  isi  elib  elib
    2. A. G. Sergeev, “Adiabatic limit for hyperbolic Ginzburg–Landau equations”, Journal of Mathematical Sciences, 202:6 (2014), 887–896  mathnet  crossref
    3. A. G. Sergeev, “Adiabatic limit in the Ginzburg–Landau and Seiberg–Witten equations”, Proc. Steklov Inst. Math., 289 (2015), 227–285  mathnet  crossref  crossref  isi  elib
    4. A. G. Sergeev, “On two geometric problems arising in mathematical physics”, J. Math. Sci., 223:6 (2017), 756–762  mathnet  crossref  mathscinet  elib
    5. A. Sergeev, “Adiabatic limit in Ginzburg-Landau and Seiberg-Witten equations”, Geometric Methods in Physics, Trends in Mathematics, eds. P. Kielanowski, S. Ali, P. Bieliavsky, A. Odzijewicz, M. Schlichenmaier, T. Voronov, Springer Int Publishing Ag, 2016, 321–330  crossref  mathscinet  zmath  isi
    6. A. Sergeev, “Seiberg-Witten theory as a complex version of Abelian Higgs model”, Sci. China-Math., 60:6, SI (2017), 1089–1100  crossref  mathscinet  zmath  isi  scopus
    7. A. Sergeev, “Adiabatic limit in Abelian Higgs model with application to Seiberg-Witten equations”, Phys. Part. Nuclei Lett., 14:2 (2017), 341–346  crossref  isi  scopus
    8. A. G. Sergeev, “Adiabatic limit in Ginzburg–Landau and Seiberg–Witten equations”, Theoret. and Math. Phys., 203:1 (2020), 561–568  mathnet  crossref  crossref  isi  elib
  • Trudy Moskovskogo Matematicheskogo Obshchestva
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