On separation of variables in gluodynamics

We study the separation of variables in S U ( 2 ) gluodynamics and the gauged S U ( 2 ) -Higgs nonlinear σ -model. Applying the Coulomb gauge we find Hamiltonian densities in terms of radial functions. We discuss the possibility of existence of D = 2 and D = 3 Yang–Mills solitons which can be relevant to extended gluonic strings in mesons (in 2D) and glueball states (in 3D). Finally separation of variables and the Hamiltonian density are presented for the 3D gauged S U ( 2 ) -Higgs nonlinear σ -model.