Many long-standing problems in basic physics require theoretical methods that can deal with strong interactions in a controlled manner. Prominent examples are the problem of confinement and chiral symmetry in quantum chromodynamics (the theory of the strong force) or condensate formation in fermionic particle systems. We develop and apply new theoretical methods to meet the challenges of strongly interacting systems. We work with various numerical and analytical tools such as lattice quantum field theory and functional renormalization methods. Our goal is to solve problems with strong coupling in particle physics and complex multibody systems.
The fundamental interactions of nature are determined by symmetries. The observable properties of physical systems can support different manifestations of these symmetries. Phase transitions often characterize the transition of a physical system from one symmetry state to another. These transitions themselves contain important information about the relevant degrees of freedom of physical systems. We investigate the symmetries of physical systems as they occur in relativistic particle physics or many-particle physics. Of particular interest are chiral symmetries, local calibration symmetries and supersymmetry. Phase transitions corresponding to a spontaneous or dynamic breaking of such symmetries are closely related to profound questions such as the generation of mass in the universe and many other properties of particle diversity in nature.