RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2006, Volume 18, Issue 1, Pages 3–33 (Mi aa58)

Expository Surveys

Geometry and analysis in nonlinear sigma models

D. Aucklya, L. Kapitanskib, J. M. Speightc

a Department of Mathematics, Kansas State University, Manhattan, Kansas USA
b Department of Mathematics, University of Miami, Coral Gabels, Florida, USA
c Department of Pure Mathematics, University of Leeds, Leeds, England

Abstract: The configuration space of a nonlinear sigma model is the space of maps from one manifold to another. This paper reviews the authors' work on nonlinear sigma models with target a homogeneous space. It begins with a description of the components, fundamental group, and cohomology of such configuration spaces, together with the physical interpretations of these results. The topological arguments given generalize to Sobolev maps. The advantages of representing homogeneous-space-valued maps by flat connections are described, with applications to the homotopy theory of Sobolev maps, and minimization problems for the Skyrme and Faddeev functionals. The paper concludes with some speculation about the possibility of using these techniques to define new invariants of manifolds.

Full text: PDF file (300 kB)
References: PDF file   HTML file

English version:
St. Petersburg Mathematical Journal, 2007, 18:1, 1–19

Bibliographic databases:

MSC: 81T13

Citation: D. Auckly, L. Kapitanski, J. M. Speight, “Geometry and analysis in nonlinear sigma models”, Algebra i Analiz, 18:1 (2006), 3–33; St. Petersburg Math. J., 18:1 (2007), 1–19

Citation in format AMSBIB
\Bibitem{AucKapSpe06}
\by D.~Auckly, L.~Kapitanski, J.~M.~Speight
\paper Geometry and analysis in nonlinear sigma models
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 1
\pages 3--33
\mathnet{http://mi.mathnet.ru/aa58}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2225211}
\zmath{https://zbmath.org/?q=an:1118.58008}
\elib{http://elibrary.ru/item.asp?id=9212597}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 1
\pages 1--19
\crossref{https://doi.org/10.1090/S1061-0022-06-00940-X}

• http://mi.mathnet.ru/eng/aa58
• http://mi.mathnet.ru/eng/aa/v18/i1/p3

 SHARE:

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. Kholodenko A.L., “Veneziano amplitudes, spin chains, and string models”, Int. J. Geom. Methods Mod. Phys., 6:5 (2009), 769–803
2. Kholodenko A., “Veneziano amplitudes, spin chains and Abelian reduction of QCD”, J. Geom. Phys., 59:5 (2009), 600–619
3. Liu Luofei, “Homotopy counting $S^1$- and $S^2$-valued maps with prescribed dilatation”, Bull. Lond. Math. Soc., 41 (2009), 124–136
4. Auckly D., Kapitanski L., “The Pontrjagin–Hopf invariants for Sobolev maps”, Commun. Contemp. Math., 12:1 (2010), 121–181
5. Kapitanski L., “Analytic Form of the Pontrjagin-Hopf Invariants”, Complex Analysis and Dynamical Systems IV, Pt 2: General Relativity, Geometry, and Pde, Contemporary Mathematics, 554, eds. Agranovsky M., BenArtzi M., Galloway G., Karp L., Reich S., Shoikhet D., Weinstein G., Zalcman L., Amer Mathematical Soc, 2011, 105–113
•  Number of views: This page: 441 Full text: 193 References: 45 First page: 1