doi:10.1016/j.physletb.2005.11.034engFalomir, H.Gamboa, J.López-Sarrión, J.Méndez, F.Da Silva, A.J.Vortices, infrared effects and Lorentz invariance violationART-2006-142388The Yang–Mills theory with non-commutative fields is constructed following Hamiltonian and Lagrangian methods. This modification of the standard Yang–Mills theory produces spatially localized solutions very similar to those of the standard non-Abelian gauge theories. This modification of the Yang–Mills theory contain in addition to the standard contribution, the term θ µ µνρλ(A Fν ρλ + 2 3A A A ) ν ρ λ where θµ is a given space-like constant vector with canonical dimension of energy. The Aµ field rescaling and the choice θµ = (0, 0, 0, θ), suggest the equivalence between the Yang–Mills–Chern–Simons theory in 2 + 1 dimensions and QCD in 3 + 1 dimensions in the heavy fermionic excitations limit. Thus, the Yang–Mills–Chern–Simons theory in 2 + 1 dimensions could be a codified way to QCD with only heavy quarks. The classical solutions of the modified Yang–Mills theory for the SU(2) gauge group are explicitly studied2006http://zaguan.unizar.es/record/15044110.1016/j.physletb.2005.11.034http://zaguan.unizar.es/record/150441oai:zaguan.unizar.es:150441Physics Letters B 632, 5-6 (2006), 740-744byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess