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Vortices, Infrared effects and Lorentz Invariance Violation

H. Falomir·J. Gamboa·J. Lopez-Sarrion·F. Mendez·A. J. da Silva
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Abstract

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 $θ^με_{μνρλ} (A^νF^{ρλ} + {2/3} A_νA_ρA_λ)$ where $θ_μ$ is a given space-like constant vector with canonical dimension of energy. The $A_μ$ field rescaling and the choice $θ_μ=(0,0,0,θ)$, 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.

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H. Falomir, J. Gamboa, J. Lopez-Sarrion, F. Mendez, A. J. da Silva. 2005-11-16. Vortices, Infrared effects and Lorentz Invariance Violation. https://doi.org/10.1016/j.physletb.2005.11.034

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