Vortices, infrared effects and Lorentz invariance violation

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 theta(mu)is an element of(mu nu rho lambda)(A(nu)F(rho lambda) + 2/3 A(nu)A(rho)A(lambda)) where theta(mu) is 3 P a given space-like constant vector with canonical dimension of energy. The A(mu) field rescaling and the choice theta(mu) = (0, 0, 0, theta), suggest the equivalence between the Yang-Mills-Chem-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 + I 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. (c) 2005 Elsevier B.V. All rights reserved.