My primary research background is in quantum field theories which has applications to a broad range of physics from high energy physics to material science.
Most of my previous work was on quantum field theories on non-commutative spaces and matrix models. Both areas are closely related, and deal with physics beyond the Standard Model by providing a mathematical framework aiming at combining quantum field theory and gravity. Additionally, non-commutative quantum field theory methods may have applications to other topics in physics such as the Quantum Hall Effect.
I have also worked on neutrino quantum kinetics, with applications to the early universe and supernovae, as well as on quantum anomalies, such as the conformal (or trace) anomaly of the energy-momentum tensor, which is expected to play a significant role near black hole horizons. More recently I applied quantum field theory methods to the interaction of dislocations (i.e. line defects) with phonons in metals, one of the dominating mechanisms defining the strength of a crystal in extreme stress conditions.

• Dislocations in Metals and Metal Plasticity
  Designing materials with good resistance to high strain rate deformation is important for a number of applications: e.g. to protect against micrometeorites for satellites, high-speed particle impact for jet engine turbine blades, etc. Plastic deformation in crystalline materials is governed by dislocations (line defects) and at high stress and temperature their mobility becomes increasingly important, as it determines the glide time between obstacles (grain boundaries, impurities, other defects, etc.) The deformation rate (resp. strain rate) of a crystal (such as a metal) is proportional to the product of mobile dislocation density and average velocity; this is captured by Orowan's relation. At very high stress, the dominating effect impeding dislocation motion is the dissipative scattering of phonons (termed `phonon wind'). This leads to non-linear `drag coefficient' $B$ which in analogy to a friction constant is defined as the driving force experienced by the dislocation over its velocity. However, this analogy is somewhat misleading having its roots in a stress regime (the `viscous regime') where $B$ is indeed almost constant. In general, $B$ is a non-linear function of velocity (and thereby resolved shear stress): In fact, a series of my more recent publications focused on the first-principles theory of dislocation drag; see e.g. J. Appl. Phys. 130 (2021) 015901, Phil. Mag. 100 (2020) 571-600, Materials 12 (2019) 948, J. Phys. Chem. Solids 124 (2019) 24, as well as Prog. Mat. Sci. 31 (1988) 1 and Int. Mater. Rev. 66 (2020) 215-255 for an extensive review.
   
• Neutrino Quantum Kinetics:
  Neutrinos, produced copiously in the early universe and astrophysical sites, can be treated in kinetic transport theory, appropriately extended to include quantum effects related to spin and flavor. In arXiv:1605.09383 (which appeared as an Editors' Suggestion in Phys. Rev. D94 (2016) 033009) we described how neutrino interactions in environments containing neutrinos, charged leptons, and nuclei affect energy-transfer as well as flavor and spin decoherence.
   
• Emergent Gravity - Geometry as a semi-classical effect:
  Formulated in terms of matrix models, one can show that (quantum) gravity actually "emerges" naturally, and in the semi-classical limit classical General Relativity terms (such as Einstein-Hilbert) are recovered.
  In the simplest case, the matrices of Yang-Mills type matrix models represent generalized "coordinates", some of which (in a "semi-classical limit") define an embedding of our non-commutative 4-dimensional space-time in a higher dimensional space. A non-trivial effective metric which depends on the non-commutativity, i.e. gravity, is then induced.
  A particularly interesting matrix model which additionally also incorporates gauge fields and fermions coupled to quantum gravity, is given by the (supersymmetric) so-called IKKT model.
   
• Quantum Field Theory on non-commutative spaces (NC QFT):
  Non-commutative space, or the direct quantization of space and time appears as a certain limit within string theory (on D-branes with string background $B$ field, somewhat reminiscent of the well-known Landau problem), or can be viewed as an independent theory of quantum gravity and an alternative to string theory or loop quantum gravity. In the latter case, it is crucial to find a theory that is renormalizable (in order to be consistent to all loop orders); this has only been achieved and proved for certain scalar cases (like e.g. the Grosse-Wulkenhaar model). In general non-commutative quantum field theories exhibit new kinds of non-local infrared (IR) divergences preventing them from being renormalizable.
  The aim, therefore, is not only to find a renormalizable non-commutative gauge field model, but also to develop new tools to actually proof its renormalizability, as current methods either break gauge symmetry or require local field theories.
  A promising model my collaborators and I have put forward is a gauge theory with a non-local additional term in the action (reminiscent of the Gribov-Zwanziger action in QCD) which improves the IR behavior through a "damping mechanism" involving modified propagators. Such a mechanism is known from according scalar models which have been shown to be renormalizable.
   
• Introductory literature/review articles to NC QFT:
  my lecture notes to the course I taught in the spring of 2011,
  SIGMA 6 (2010) 062, arXiv:0705.0705,
  arXiv:hep-th/0109162 (Phys. Rept. 378 (2003) 207),
  arXiv:hep-th/9701078 (Lect. Notes Phys. m51 (1997) 1),
  arXiv:1003.4134 (Class. Quant. Grav. 27 (2010) 133001).
   

Apart from these special topics, I am interested in Physics beyond the Standard Model in general, as well as gravity, black holes, quantum anomalies, QCD, the Quantum Hall effect, and Neutrino oscillations.