Strong interactions in between particles and/or fields cause strong correlations. To understand the physical implications of those correlations within different quantum field theories, functional methods are employed to derive equations for the correlation functions of the theory. Employing analytical studies of the exact equations as well as numerical solutions of suitably approximated sets of equations important properties of the correlation functions can be extracted and applied to different physical systems.
The correlation functions of Quantum Chromo Dynamics (QCD) allow to study properties of hadrons as masses and form factors as well as (some examples of) decays. Allowing for non-vanishing temperatures and densities the phases of QCD and the properties of hot and dense strongly-interacting matter can be investigated.
Extending these techniques from QCD to similarly strongly-interacting quantum gauge field theories technicolour and related beyond-the-Standard-Model scenarios are studied with the aim to shed light on the possibility that the Higgs particle is not elementary but composite.
Not only strong interactions but also strong fields cause strong correlations with interesting consequences. An important example of such effects is given by the spontaneous particle pair creation in ultra-strong electromagnetic fields. Due to the rapid development of laser technology, theoretical predictions obtained on the basis of correlations functions, such as particle production rates and spectra, can be in the near future compared with experiment.
Strong interactions may also imply the internal consistency of quantum field theories which are seemingly ill-defined on a perturbative level. The latter property also applies to parts of the Standard Model (SM) of Particle Physics. Functional methods, and thereby especially the Functional Renormalisation Group, are employed to study whether there is the exciting possibility that the SM and/or the SM together with gravity are complete are consistent theories without any further theoretical need for beyond-the-Standard-Model physics.
Above the chiral symmetry restoration crossover at high temperatures Quantum Chromo Dynamics (QCD) is characterised by a symmetry of the color charge, which means that QCD is still in a confining mode. It is not a quark-gluon-plasma (QGP) as was long thought. We attempt to understand properties of QCD in this regime and a smooth transition to QGP that happens at much higher temperature.
Our primary research area is to create a bridge from a fundamental understanding of quantum gauge theories to their phenomenology. The particular aim is to identify and understand phenomena, which cannot be captured with standard perturbative means, and how they manifest the genuine non-linear structure of quantum theories. Hereby we cover topics like Higgs physics at CERN, dark matter, searches for new physics like grand-unified theories, and quantum gravity.
Our story so far can be read in two reviews articles, on "Brout-Englert-Higgs physics: From foundations to phenomenology"  and "Gauge bosons at zero and finite temperature" . A popular science description of this research can also be found in our blog . The latest news on our research or from the field can also be found on Twitter .
Quantum chromodynamics (QCD), the fundamental theory underlying the nuclear forces, is a highly non-linear quantum field theory. Its ab-initio solution is an enormous task which can even exhaust the capacity of modern high-performance computer systems. Phenomenological problems in strong-interaction physics are therefore often tackled by means of effective theories which resemble a few basic properties of QCD, but exhibit less degrees of freedom. Constituent-quark models, e.g., fall into this category. Within constituent-quark models hadrons are considered as bound states of a few quarks and antiquarks. Such models provide predictions for hadron masses, the electroweak structure of hadrons and even strong decays of hadrons. The theoretical framework, when dealing with constituent-quark models, is in our case relativistic quantum mechanics . We are also interested in exclusive hadronic reactions at high energies which can be treated by means of perturbative QCD. Reactions, like photo- and electroproduction of hadrons, can provide information on the structure of hadrons not accessible by simple constituent-quark models.
 W.H. Klink und W. Schweiger, W.: Relativity, Symmetry, and the Structure of Quantum Theory: Volume 2 (Point Form Relativistic Quantum Mechanics),
Morgan & Claypool Publishers, Bristol (2018). doi:10.1088/978-1-6817-4891-7
Lattice simulations of Quantum chromodynamics (QCD) provide a very versatile non-perturbative tool based on the importance sampling method. At nonzero quark chemical potential such calculations are hampered by the sign problem: the measure of the theory becomes non-positive, thus importance sampling breaks down. We develop the Complex Langevin method which deals with the problem by extension to a complexified field manifold, using analytichal continuation. The method can be applied generally to many theories which suffer from a sign problem.
See  for a short review of the idea of complexification, [2,3] for our most recent results on the phase diagram of QCD.
 D. Sexty, "New algorithms for finite density QCD" PoS LATTICE2014 (2014), 016 doi:10.22323/1.214.0016, arxiv.org/abs/1410.8813
 D. Sexty, "Calculating the equation of state of dense quark-gluon plasma using the complex Langevin equation", Phys. Rev. D100 (2019) no.7, 074503, doi:10.1103/PhysRevD.100.074503, arxiv.org/abs/1907.08712
 M. Scherzer, D. Sexty and I.-O. Stamatescu, "Deconfinement transition line with the Complex Langevin equation up to $\mu /T \sim 5$", Phys. Rev. D102 (2020) no.1, 014515, doi:10.1103/PhysRevD.102.014515, https://arxiv.org/abs/2004.05372