Field theoretic study of electron-electron interaction effects in Dirac liquids

The aim of this habilitation thesis is to present recent results, obtained during the period 2012-2017, related to interaction effects in condensed matter physics systems such as planar Dirac liquids, e.g., graphene and graphene-like systems, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems (for their Dirac composite fermions). These liquids are characterized by gapless bands, strong electron-electron interactions and emergent Lorentz invariance deep in the infra-red. We address a number of important issues raised by experiments on these systems covering subjects of wide current interest in low-energy (condensed matter) as well as high-energy (particle) physics. We shall consider in particular the subtle influence of interactions on transport properties and their supposedly crucial influence on a potential dynamical mass generation. The resolution of these problems will guide us from the thorough examination of the perturbative structure of gauge field theories to the development and application of non-perturbative approaches known from quantum electro/chromo-dynamics to address strong coupling issues.