Lines vortices in the \(U(1)\)-Higgs model. (English) Zbl 0874.53019

Riviere, Tristan

ESAIM, Control Optim. Calc. Var. 1, 77-167 (1996).

From the paper: “For a given U(1)-bundle \(E\) over \(M=\mathbb{R}^3\setminus \{x_1,\dots,x_n\}\), where the \(x_i\) are \(n\) distinct points of \(\mathbb{R}^3\), we minimise the U(1)-Higgs action and we make an asymptotic analysis of the minimizers when the coupling constant tends to infinity. We prove that the curvature (= magnetic field) converges to a limiting curvature that we give explicitly and which is singular along line vortices which connect the \(x_i\)”.

Reviewer: J.Muciño-Raymundo (Morelia)

MSC:

53C07	Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
53C21	Methods of global Riemannian geometry, including PDE methods; curvature restrictions

Keywords:

Higgs field; Ginzburg-Landau equations

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