Dressed Dirac propagator in a BRST framework

In this Master thesis, the work done under the guidance of Prof. Olindo Corradini is reported. The master thesis project aims to describe the propagation of a Dirac (and scalar) particle that interacts with external fields in the Worldline formalism and by using the BRST method described below. For the computations an external electromagnetic field has been chosen; however, due to the generality of the method, it is possible to perform similar computations for other kind of interactions. The main object that describes the propagation of a particle is the propagator. When external interactions are taken into account, the computation of such an object becomes mathematically complicated because of the presence of an integral over an arbitrary function. This arbitrariness arises from the possible choice on the form of the external field, and in order to do the computations, it is thus necessary to fix a form of the field; a very common choice being a sum over plane waves. However, thanks to the LSZ formula, it is possible to write the amputated propagator in such a way that the integral is replaced by a derivative and where the integration variable is taken to +∞.