The natural theoretical framework for particle physics is quantum field theory, in which the so-called renormalization procedure is required in order to calculate measurable quantities. We investigate various aspects of non-pertur- bative renormalization.
One cannot obtain physical results in quantum field theory (QFT) without renormalization, and the formalism needs to be extended to the renormalization group (RG) in order to understand the physics of quantum field theories on different length or momentum scales. The RG analysis is thus of importance in other applications, in the main applica- tion of QFT, which was originally centred in particle physics. Renormalization can be performed by the functional RG method, which is a non-perturbative technique. On the one hand, we use the functional RG approach to perform the renormalization of sine-Gordon-type scalar theories, which find important applications, not only in particle physics, but also in condensed matter systems such as high-temperature superconductors. On the other hand, we study the technique itself – more precisely, we improve the predictive power of functional RG by optimising the one of its most important unsolved problems – the regulator-dependence.