Speaker
Description
In order to explore key problems in particle physics such as hadron spectroscopy, confinement and dynamical mass generation, we require a non-perturbative approach to describing our particle interactions. In quantum field theory, this is tantamount to understanding the full non-perturbative structure of the fermion and photon propagators, which in turn requires knowledge of the fermion-photon vertex. Moreover, these fully determined functions would require a consistent solution at all orders of the infinite tower of Schwinger-Dyson equations, thus it is often the case that some approximation, or truncation, is required. Here, we intend to build a vertex structure that is consistent up to next-to-leading order. By introducing an ansatz into the massless fermion and photon Schwinger-Dyson equations, and demanding multiplicative renormalisability, we constrain this vertex structure at both the non-perturbative and order-by-order levels. Furthermore, we enforce a correct small-coupling limit to be in accordance with 2-loop perturbative calculations. We subsequently find a set of consistent vertex structures, as well as the next-to-leading order structures of the massless fermion and photon propagators.