On the space-time monopole equation
| Autor: | Bo Dai, Karen Uhlenbeck, Chuu-Lian Terng |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Mathematics - Differential Geometry
37K15 37K25 37K35 Scattering High Energy Physics::Lattice Space time Lorentz transformation 010102 general mathematics Magnetic monopole FOS: Physical sciences Mathematical Physics (math-ph) 01 natural sciences Action (physics) 010101 applied mathematics symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems Differential Geometry (math.DG) Inverse scattering problem FOS: Mathematics symbols 0101 mathematics Hamiltonian (quantum mechanics) Mathematical Physics Mathematics Mathematical physics Gauge fixing |
| Zdroj: | Surveys in Differential Geometry. 10:1-30 |
| ISSN: | 2164-4713 1052-9233 |
| DOI: | 10.4310/sdg.2005.v10.n1.a1 |
| Popis: | The space-time monopole equation is obtained from a dimension reduction of the anti-self dual Yang-Mills equation on $\R^{2,2}$. A family of Ward equations is obtained by gauge fixing from the monopole equation. In this paper, we give an introduction and a survey of the space-time monopole equation. Included are alternative explanations of results of Ward, Fokas-Ioannidou, Villarroel and Zakhorov-Mikhailov. The equations are formulated in terms of a number of equivalent Lax pairs; we make use of the natural Lorentz action on the Lax pairs and frames. A new Hamiltonian formulation for the Ward equations is introduced. We outline both scattering and inverse scattering theory and use B\"acklund transformations to construct a large class of monopoles which are global in time and have both continuous and discrete scattering data. Comment: 31 pages |
| Databáze: | OpenAIRE |
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