  The Yang-Mills theory with noncommutative fields is constructed following
Hamiltonian and lagrangean methods. This modification of the standard
Yang-Mills theory shed light on the confinement mechanism viewed as a Lorentz
invariance violation (LIV) effect. The modified Yang-Mills theory contain in
addition to the standard contribution, the term $\theta^\mu \epsilon_{\mu \nu
\rho \lambda} (A^\nu F^{\rho \lambda} + {2/3} A_\nu A_\rho A_\lambda)$ where
$\theta_\mu$ is a given space-like constant vector with canonical dimension of
energy. The $A_\mu$ field rescaling and the choice $\theta_\mu=(0,0,0,\theta)$,
one can show that the modified Yang-Mills theory in 3+1 dimensions can be made
equivalent to a Yang-Mills-Chern-Simons theory in 2+1 dimensions if one
consider only heavy fermionic excitations. Thus, the Yang-Mills-Chern-Simons
theory in 2+1 dimensions is a codified way of ${QCD}$ that include only heavy
quarks. The classical solutions of the modified Yang-Mills theory for the SU(2)
gauge group are confining ones.
