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<SUP>μ</SUP>ε<SUB>μνρλ</SUB> (A<SUP>ν</SUP> F<SUP>ρλ</SUP> + 2/3 A<SUB>ν</SUB> A<SUB>ρ</SUB> A<SUB>λ</SUB>) where θ<SUB>μ</SUB> is a given space-like constant vector with canonical dimension of energy. The A<SUB>μ</SUB> field rescaling and the choice θ<SUB>μ</SUB>=(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.