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In this work, the conversion of linear polarization of a laser beam to circular one through its forward scattering by a TeV order charged lepton beam in the presence of Lorentz violation correction is explored. We calculate the ratio of circular polarization to linear one (Faraday conversion phase ï¿½?ï¿½?FC ) of the laser beam interacting with either electron or the muon beam in the framework of the quantum Boltzmann equation. Regarding the experimentally available sensitivity to the Faraday conversion ï¿½?ï¿½?FCï¿½??10ï¿½??3ï¿½??10ï¿½??2 , we show that the scattering of a linearly polarized laser beam with energy k0ï¿½?ï¿½0.1 eV and an electron/muon beam with flux ÏµÂ¯e,Î¼ï¿½?ï¿½1010/1012 TeV cm ï¿½??2 s ï¿½??1 places an upper bound on the combination of lepton sector Lorentz violation coefficients cÎ¼Î½ components (cTT+1.4 c(TZ)+0.25(cXX+cYY+2 cZZ) . The obtained bound on the combination for the electron beam is at the 4.35ï¿½?10ï¿½??15 level and for the muon beam at the 3.9ï¿½?10ï¿½??13 level. It should be mentioned that the laser and charged lepton beams considered here to reach the experimentally measurable ï¿½?ï¿½?FC are currently available or will be accessible in the near future. This study provides a valuable supplementary to other theoretical and experimental frameworks for measuring and constraining Lorentz violation coefficients.
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