SOLVING THE MODIFIED DIRAC EQUATION FOR MUON MOVING IN STRONG BACKGROUND ELECTRIC FIELD

Abstract

In this thesis, the covariant form of Dirac equation has been modified for a relativistic muon by incorporating the uniform background electric field through the principle of minimal coupling. The Electromagnetic (EM) field has been gauged so as to produce a constant electric field pointing in a particular direction, and a vanishing magnetic field. Then the modified Dirac equation has been manipulated using separation of variables to take the form the Weber’s differential equation for which the parabolic cylinder functions (PCFs) are solutions. Finally, the general form of spin-sum has been derived for two spin states. Unlike the background magnetic field the presence of electric field has failed to produce discrete energy eigenstates, which means fermions moving in a latter field behave like classical particles. Moreover, the derived spin sum shows strong dependence on the background electric field