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 μεμνρλ(AνF ρλ+2/3AνAρA 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 studied. © 2005 Elsevier B.V. All rights reserved.