Three-dimensional Yang-Mills-Higgs equations in gauge-invariant variables (Q1326815)

The author proposes a formulation of three-dimensional \(SU (2)\) and \(SO (1,2)\) Yang-Mills theories in the gauge-invariant variables \(G_{ij} = \text{tr}^*F_ i{}^*F_ j\), where \({}^*F_ i = {1 \over 2} \varepsilon_{ijk} F^{jk}\) is the tensor dual to \(F^{ij}\). It is shown that the tensor \(G_{ij}\) satisfies three-dimensional equations with simple right-hand side and \(G_{ij}\) playing the role of a new metric on spacetime. This result is generalized to the case of a system of Yang-Mills-Higgs fields.