Quantum electrodynamics of multiple dirac particle systems

Low energy bound state systems consisting of Relativistic Dirac particles are one of the main problems of Quantum Electrodynamics. In this thesis, mathematical models are developed for unstable systems such as Positronium, Exciton, Positronium-ion and Charged-Exciton, consisting of $ 2 $ and $ 3 $ Dirac particles with equal mass. These developed mathematical models are based on the exact solutions of the $2$ and $3$-body Dirac equations, which are derived from Quantum Electrodynamics in fully-covariant form via the Action principle. In a few space-time backgrounds with different physical properties, the dynamics of neutral composite systems formed by an interacting fermion-antifermion pair have been investigated and some contradictory results in the literature can be explained, by showing that the obtained results support each other. With the expansion of the mathematical model developed for fermion-fermion systems, the dynamics of the systems consisting of interacting $3$ relativistic fermions were examined and a general Energy spectrum was obtained.