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Abstract

In this Thesis, an alternate mathematical formalism for the study of radiative corrections in atomic physics has been developed. In this context, highly charged ions (HCIs) are studied, where the effect of such QED corrections become very evident and allow for precision experiments. The Coulomb interaction between electron and nucleus leads to bound states that are innately non-perturbative and requires the inclusion of the localizing nuclear potential in the zeroth order of the Dirac equation. This is implemented by constructing the propagators of QED processes in a strong Coulomb field using functional integrals. The free propagators and the Dirac-Coulomb Green’s function (DCGF), the central entity of bound-state QED, are derived in closed analytical forms. The closed forms are then used to construct the formal theory of the Lamb shift at the one-loop level using Schwinger-Dyson equations. Vacuum-polarization correction to the bound-state energy levels is studied using perturbative path integrals, where the Uehling potential is treated as a local perturbing potential. Within the same framework, the self-energy corrected bound-electron propagator is determined. The energy-level shifts are then obtained through methods of complex contour integration and computed numerically using finite basis sets. From the numerical results we identify a range of ions enabling the novel observation of QED effects via precision mass spectrometry.