In this thesis, we will investigate the effects of non-commutative and magnetic field as back ground field on the some most important interactions of elementary particles. In non-commutative case, we will show that by considering QCD and QED interactions together, Beta function of NCQED can obtain zero, negative and plus values. In case of back ground magnetic field, we will study and calculate the effects of weak, ordinary and strong magnetic field on some physical systems. For strong magnetic field, we calculate the probably effects of this magnetic field on distributions of nucleons and electrons as constituent particles of neutron star and show the ratio number neutrons to number protons reduce in presence of magnetic field. Also we will obtain the electric potential and electric fields by using Thomas-Fermi equation, modified Poisson equation for complete degeneracy system of electrons and nucleons, and then we will show the electric field in presence of magnetic field increases (at surface of neutron star). Farther more we will see the maximum electron Fermi energy to keep all of electron in side of neutron star in magnetic field have the same value with the case without magnetic field. Finally we will investigate the effects of strong magnetic field for cooling step of neutron star, spatially we will calculate neutrino emissivity in during “ ” process and we will see this quantity increases in presence of strong magnetic field (this process is one of most important for cooling step) for example when the magnetic field is about Gauss, the rate lost energy by “ ” grows up to one order magnitude. For weak magnetic field, we will try to consider the effects of very weak magnetic (about micro gauss) present in back ground cosmic on the polarization of cosmic microwave background (CMB) and for this case we will show magnetic field due to produce circular polarization for CMB photons whereas in order to produce circular polarization doesn’t need primary linear polarization for CMB photons and the end we will obtain a value about ? for Faraday conversion phase shift in presence of magnetic field. Finally for ordinary magnetic field, we will consider the effects of magnetic field (present in experience to measure electron and muon g-factor) on electron and muon magnetic moment and we will obtain a correction about for electron g-factor and a correction about for muon g-factor from transformed momentum due to background magnetic field. Keywords : Background Fields, Non-commutative Space-Time, Magnetic Field, Beta Function, Neutron Star, Thomas-Fermi Equation, Cooling Step, CMB Photons, Circular Polarization, Electron and Muon g- Factors.
