Geodesic
Three-dimensional Yang--Mills--Higgs equations in gauge-invariant variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 1, pp. 66-75

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A formulation of three-dimensional $SU(2)$- and $SO(1, 2)$ Yang–Mills theories in the gauge-invariant variables $G_{ij} =\hbox {tr}^*F_i^*F_j$ is proposed. It is shown that the tensor $G_{ij}$ satisfies three-dimensional Einstein equations with simple right-hand side and $G_{ij}$ playing the role of a metric. This result is generalized to the case of a system of Yang–Mills–Higgs fields. 
@article{TMF_1993_94_1_a4,
     author = {F. A. Lunev},
     title = {Three-dimensional {Yang--Mills--Higgs} equations in gauge-invariant variables},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {66--75},
     publisher = {mathdoc},
     volume = {94},
     number = {1},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_94_1_a4/}
}
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F. A. Lunev. Three-dimensional Yang--Mills--Higgs equations in gauge-invariant variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 1, pp. 66-75. http://geodesic.mathdoc.fr/item/TMF_1993_94_1_a4/