This thesis is involved to study phenomenological aspects of New Physics (NP) in the Standard M odel Extension (SME) frame. One has introduced t he SME as a frame that contains all the Lorentz Violation (LV) interactions. Then, Non-Commutative Standard Model (NCSM) have shown with Sieberg- Witten structure where could violate Lorentz symmetry intrinsically. We've found a corresponding between the NCSM and SME in the present electromagnetic background fields. Here, we've considered only the electroweak sector of Standard Model (SM) in both theories and derived all the LV parameters in the NC parameter and background field terms. Furthermore, we've studied all the components of LV parameters in the fixed and rotated frames. We could find bound on both components of NC parameter and LV parameters in the current studies. Studying on the charged lepton Electric Dipole Moment (EDM) in the SME frame is a part of the thesis. Particles EDM leads to CP Violation (CPV). The arameter as a source of CPV in the SME and can enhance in high energy limit in the present of Lorentz symmetry breaking. We have calculated cross-section of electron-positron annihilation process and Bhabha scattering and found the bounds on combination , and for tau, muon, and electron, respectively from the LEP collider results. We've predicted bounds from ILC experiment, as well . We have investigated Anomalous Magnetic Dipole Moment (AMDM) of muon in the SME by parameter. W e have constructed QEDE with this parameter and introduced all the electromagnetic form factors. By considering the deviation of Muon- AMDM comes from LV at high energy level, one has found the would be as order of where it is a compatible bound. Other form factors have studied in this chapter and showed how to cancel the IR and UV divergences. Finally, we have shown an expression between EDM of particles and CPV phase in the effective field theory. We have estimated CPV phase order in the present of LV background by results of the EDM and AMDM form factors in the previous chapters. It would motivate to study this CPV phase where explain the baryogenesis and study some other ideas for the next researches.
