Without experimentalists, theorists tend to drift, without theorists experimentalists tend to falter.

Research interests

The overarching focus of my research lies in properties of strongly interacting matter. Specifically, I am interested in properties of excited states of matter, short-lived excitations of hadrons such as protons, pions etc..

My main research goal lies in building a "tridge" (three-sided bridge) between (1) theoretical methods based on symmetries of the strong interaction interaction, (2) phenomenology and application to experimental observations and (3) results of numerical ab-initio calculations of Lattice QCD.

If you want to know more see the sources below. They are ordered with respect to the desired level of details:

• General audience, no physics background knowledge required:
  Presentation-slides (in German)
• Beginning student level:
  Contribution to Encyclopedia of Particle Physics: "Theory of resonances"
• Advanced student level:
  Physics Reports Review: "Towards a theory of hadron resonances"
• Specialized reviews:
  (a) "Review of the \(\Lambda\)(1405) A curious case of a strangeness resonances"
  (b) "Multi-particle systems on the lattice and chiral extrapolations: a brief review"
  (c) "Dynamical coupled-channel models for hadron dynamics"

For a full list of my publications see iNSPIREhep (mostly open source). Some topics are also highlighted below in simple language.

Lattice QCD (a lab in a computer)

One of the currently best ways to access QCD at low energies while taking into account its non-perturbative nature is the lattice gauge theory. In the nutshell it is based on the discretization of the 4D-spacetime by an Euclidean 4D discrete lattice in a finite volume. Quarks are allowed to live only on the intersections of the lattice sites while gluons are associated with the links between the intersections. Through a series of well-defined steps (see fig. to the right for an excerpt) physical information can be accessed in a numerical calculation performed in supercomputing facilities. For an introductory lecture on the techniques as well as historical details see, e.g., [LectureNotes].

I am interested in relating the results of lattice QCD to the phenomenological ones based on experimental observations. A central object of study hereby is the so-called quantization condition which relates real energy eigenvalues of a multi-particle system in a finite volume with complex-valued scattering amplitudes. Based on continuum Quantum Field Theory principles we have derived few years ago the Finite-Volume-Unitarity (FVU) approach which extends to up to three interacting particles. See figure to the left and [Review].

Effective Field Theories
S-Matrix
Non-perturbative techniques...

A powerful and systematically improvable access to QCD at low energies can be gained through the so-called Effective Field Theories. In a nutshell, the idea is to replace (integrate out) degrees of freedom which are irrelevant at the energies of interest by the effective ones. Typically, this is guided by studying the symmetries of the underlying theory and their potential breaking. In the case of QCD at low energies, the effective theory is called Chiral Perturbation Theory, see e.g. [Review, Lectures].

I have worked on developing various theoretical tools based on Chiral Perturbation Theory, particularly to study properties of the excited hadrons (strongly interacting particles). In this, S-matrix principles become another important guiding tool which are based on very fundamental symmetries of nature. For example (for more details see, e.g., "Theory of resonances"):

• In quantum field theories particles can be related to antiparticles. This relates various transition amplitudes.
• Because of the causality, these transition amplitudes are meromorphic in the kinematic variables promoted to complex values
• In any fundamental process, the probability to measure anything is per definition unity. This translates to the unitarity constraint of the transition amplitudes

One consequence of this is that transition amplitudes (objects encoding everything there is to know about a physical process) become meromorphic functions on, in general, multi-sheeted complex Riemann surface. They are bound by an observation on the real-valued boundary of a physical Riemann sheet, and can have poles on further unphysical Riemann sheets. Poles on unphysical Riemann sheets are associated with unstable states (e.g., excited hadrons). See figure to the right for a pictorial example.

The complex-valued positions of these poles do not depend on a particular process but are rather universal, encoding a unique signature of nature. The summary of humanity's knowledge in this regard is compiled by the [Particle Data Group].