# Lines vortices in the U(1) - Higgs model

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 1, page 77-167
- ISSN: 1292-8119

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topRiviere, Tristan. "Lines vortices in the U(1) - Higgs model." ESAIM: Control, Optimisation and Calculus of Variations 1 (2010): 77-167. <http://eudml.org/doc/197265>.

@article{Riviere2010,

abstract = {
For a given U(1)-bundle E over M = $\lambda _\{2\}$\{x1, ..., xn\}, where the xi are n distinct points of $\lambda _\{2\}$, 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 explicitely and which is singular along line vortices which connect the xi. This work is the three dimensional equivalent of previous works in dimension two (see [3] and [4]). The results presented here were announced in [12].
},

author = {Riviere, Tristan},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Non linear PDE / elliptic equations / abelian gauge theory / Ginzburg-Landau equations / Higgs field / variationnal problem on fiber bundle / variationnal problem in superconductivity / vortices
and singularities / harmonic maps.; Higgs field; Ginzburg-Landau equations},

language = {eng},

month = {3},

pages = {77-167},

publisher = {EDP Sciences},

title = {Lines vortices in the U(1) - Higgs model},

url = {http://eudml.org/doc/197265},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Riviere, Tristan

TI - Lines vortices in the U(1) - Higgs model

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 1

SP - 77

EP - 167

AB -
For a given U(1)-bundle E over M = $\lambda _{2}${x1, ..., xn}, where the xi are n distinct points of $\lambda _{2}$, 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 explicitely and which is singular along line vortices which connect the xi. This work is the three dimensional equivalent of previous works in dimension two (see [3] and [4]). The results presented here were announced in [12].

LA - eng

KW - Non linear PDE / elliptic equations / abelian gauge theory / Ginzburg-Landau equations / Higgs field / variationnal problem on fiber bundle / variationnal problem in superconductivity / vortices
and singularities / harmonic maps.; Higgs field; Ginzburg-Landau equations

UR - http://eudml.org/doc/197265

ER -

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