Vortices, infrared effects and Lorentz invariance violation

H. FALOMIR; J. GAMBOA; J. LÓPEZ-SARRIÓN; F. MENDEZ; A.J. DA SILVA

Physics Letters B

Lugar: Elsevier, Science@direct; Año: 2006 vol. 632 p. 740 - 744

0370-2693

The Yang-Mills theory with noncommutative 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 $ heta^mu epsilon_{mu u ho lambda} left(A^ u F^{ ho lambda} + rac{2}{3} A_ u A_ ho A_lambda ight)$ where $ heta_mu$ is a given  space-like constant vector with canonical dimension of energy.  The $A_mu$ field rescaling and the choice $ heta_mu=(0,0,0, heta)$, 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.doi:10.1016/j.physletb.2005.11.034