Vortices, infrared effects and Lorentz invariance violation

Abstract The 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 e μ ν ρ λ ( A ν F ρ λ + 2 3 A ν A ρ A λ ) where θ μ is a given space-like constant vector with canonical dimension of energy. The A μ field rescaling and the choice θ μ = ( 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 studied.