In this thesis, first an overviewof the symmetries and their characteristics in physics is presented. As for thesymmetries, we only focus on discrete symmetries of charge conjugation (C),parity (P), time reversal (T), and Lorentz because these symmetries result fromLorentz symmetry, forming the basis of the quantumfield theory. The second chapter of this thesis discusses the characteristicsof the solutions to Dirac equation in the presence of uniform magnetic fieldsbecause the shape of Dirac spinors in the presence of the magnetic fielddiffers from the vacuum state. Furthermore, we focus on the nature of thesesolutions and we study the effect of the selection of the vector potential ( ) on these solutions. In this chapter, the electron-positronscattering to muon-antimuon is studied in the presence of a strong magneticfield and it is demonstrated that the scattering cross-section ( ) on the lowest scattering order in the presence of a strongmagnetic field is determined by the inverse biquadrate of the center of mass energy ( ). However, in the vacuum state, the scattering cross-sectiondepends on the inverse quadrate of the center of mass energy ( ). Afterward, the violationof (CPT) and Lorentz symmetries is studied. Lorentz and (CPT) symmetriesare exact symmetries in nature and thus their violation leads to massiveconsequences in physics. These symmetries are not directly broken or in otherwords, the Lagrangians of particles with different spins do not have terms thatviolate these symmetries. Therefore, these Lagrangians are constantly subjected to Lorentz and (CPT) invariant transformations.
