Abstract:
This thesis provides a relativistic description of electron-positron scattering and pair
annihilation in quantum electrodynamics. By evaluating the modulus square of the invariant
matrix elements, the differential cross-section for unpolarized electron-positron elastic
scattering is calculated using leading-order Feynman diagrams. The study considers spin-half
electrons and positrons, ensuring a consistent quantum electrodynamical framework. The
relativistic expression of the spin-average invariant amplitude is constructed using Feynman
rules, Completeness relation, and trace theorems. Integration over the Dirac-delta function
reveals the dependence of the differential cross-section on the energy and scattering angle.
Theoretical predictions are verified through computer simulations, confirming the behavior of
the model. The study highlights the dominance of the t-channel contribution in the angular
distribution plots and emphasizes the importance of the scattering term in Bhabha processes.
Recommendations include exploring quantum corrections, external fields, radiative and
polarization effects, electroweak corrections, and investigating practical implications in particle
physics, astrophysics, and medical imaging
