Title: Electromagnetic Scattering In Worldline Quantum Field Theory

Abstract: In this thesis Worldline Quantum Field Theory (WQFT) is employed to examine the classical unbound two-body, i.e. scattering, problem of electromagnetically interacting point particles. The WQFT formalism allows for the systematic perturbative expansion of classical observables, which is useful in the field it originated in: the classical gravitational scattering problem. In many ways, the electromagnetic (EM) scattering problem is a simplified version of the gravitational case, which is useful for illustrating the WQFT approach.
The first part of the present work discusses the way in which the classical equations of motion give rise to WQFT Feynman diagrams – tree-level contributions to the path integral of two worldline fields and one photon field. It discusses preliminaries of the calculation of observables such as the impulse kick, the scattering angle and the radiated momentum.
These observables are then calculated order by order, which, for each order, entails new chal- lenges to be met by new techniques: expressions for diagrams must be assembled, divergent inte- grals must be dealt with via dimensional regularization, tensorial loop momenta must be rewritten via tensor reduction, scalar integrals must be solved with the use of Schwinger parametrization, master integrals must be identified with the use of Integration by Parts- and symmetry-relations and they must be solved by use of differential equations in canonical form and the method of regions.
Known values for the impulse kick could for the most part be reproduced, regrettably, however, some calculations remain erroneous and yield wrong results. The results for the Master Integrals – a small set of scalar integrals, which all others may be reduced to – at Next to Next to Leading Order could also not be reproduced.