Analytical and Numerical Methods for High-Precision Studies in Ultrarelativistic Strong-Field Quantum Electrodynamics

This thesis presents a comprehensive exploration of both analytical and numerical techniques used to model processes in ultrarelativistic strong-field quantum electrodynamics (SFQED). % We developed SFQEDtoolkit, an open-source library that employs advanced function approximation techniques to accurately model nonlinear Compton (NIC) emission and nonlinear Breit-Wheeler (NBW) pair creation processes. % Simulations combining particle-in-cell (PIC) codes with SFQEDtoolkit have been used to investigate collisions between ultrarelativistic dense electron beams and plasma targets, demonstrating that electron-positron jets exceeding solid densities can be produced within self-generated magnetic fields up to 10 MT. % These findings reveal a novel regime where SFQED, atomic, and plasma physics are intrinsically interwoven, opening a new avenue of research in SFQED. % Furthermore, we derive analytical expressions for NIC and NBW differential distributions that describe the energy, angular, spin, and polarization characteristics of the produced particles. % Notably, the derivation of these distributions, following state-of-the-art methodologies, yields results that can give negative values over certain parameter intervals, undermining their probabilistic interpretation. % We demonstrate that integrating these distributions over the ``formation time'' of the quantum process restores their conventional physical meaning. % Overall, the contributions of this thesis advance the analytical and numerical modeling of SFQED processes, providing a robust framework for forthcoming experimental studies of SFQED, which are critically relevant for extreme-field plasma physics and the microphysics of pulsars and magnetars.