My primary research discipline is Quantum Field Theory and Particle Phenomenology. In the first paragraph I will mention topics in this area that I have found especially interesting during my Master of Science study, and what I have learned about these topics. Thereafter, I will present some other topics that I found interesting during my studies without going into detail, and I will continue with a brief description of my master research project. In conclusion, I will mention topics I would like to learn more about in the future.
In the Quantum Field Theory course I studied both path integral quantization and canonical quantization: I learned to quantize theories, derived the Feynman rules for these theories and computed cross sections and decay rates for processes. I studied Quantum Electrodynamics and I learned to derive the Faddeev-Popov quantisation. I was introduced to the basics of renormalisation, specifically the dimensional analysis of Lagrangian operators and their classification in super-renormalisable, renormalisable and non-renormalisable. In the Elementary Particles course I learned about the quantisation and renormalisation of non-Abelian gauge theories and the physics of elementary particles, the microscopic building blocks of our universe. In particular, I learned the path integral quantisation of non-Abelian SU(N) gauge theories and the Standard Model of Particle Physics. Renormalisation was treated in the context of renormalised perturbation theory and I derived the beta functions of the SU(N) and U(1) gauge theories in spacetime dimensions less or equal to four, to one loop. I also learned about spontaneous symmetry breaking and the Higg’s mechanism. Furthermore, the nature of neutrinos, the oscillation phenomenon of neutrinos and the CKM matrix were extensively discussed. The latter topics were also treated in the more experimental course named Particle Physics Phenomenology. As an example of physics beyond the Standard Model, the SU(5) unification of the electroweak and strong forces was also treated in the Elementary Particles course. Of course I have read and studied, out of interest and to gain more knowledge, a lot of other topics within the area of Quantum Field Theory and Particle Phenomenology which I do not mention here.
Furthermore, I followed courses on Advanced Quantum Mechanics, Symmetries in Physics (Lie groups), Mathematical Methods in Physics, Geometry, Topology, Cosmology and General Relativity, which I also found very interesting. Later on, in my master research project, I studied Lattice Field Theory and statistical methods as a non-perturbative approach to solving Quantum Field Theories, in particular in the context of Quantum Chromodynamics, and tried to find the glueball masses in the large-N limit. I studied the N-counting rules, how it affects the original theory and phenomenological implications of the large-N limit for glueballs and mesons, which included: the OZI rule, the global anomaly in the chiral symmetry of Quantum Chromodynamics and a recently proposed exact solution of large-N Yang-Mills theory. I learned to construct glueball observables on the four-dimensional hypercube lattice, by means of Wilson loops, and how to calculate the expectation values of observables (such as the two-point connected correlator to calculates masses) on the lattice by using the Monte Carlo method (Metropolis, pseudo-heatbath and overrelaxation update schemes), whereby the links on the lattice (which represent the gluons) are represented with complex SU(N) matrices and were updated to make different lattice configurations. As a first step the self made code was successfully tested to agree with results from literature at relatively small-N for simple observables (plaquette and Wilson loop averages), and was inspected on finite volume and UV effects. Thereafter, first tests for the determination of the scalar 0(+,+) glueball mass in SU(2) were performed. However, the extraction of the glueball correlator is difficult, as noise is dominating the signal. Therefore, I studied and implemented two noise reduction algorithms, the multihit and multilevel, and used the well-known Jackknife procedure on top of that. This significantly optimized the results, but not enough to determine a clear mass, only an upper limit. From this it was found that the statistics should be increased and a high degree of improvement strategy is necessary in order to be able to measure the glueball spectrum at large-N. Furthermore, as an attempt to set the physical scale and test the code, also the string tension was studied.
Following the line of my research topic, I find it interesting to continue doing research in the vast area of Quantum Field Theory and Particle Phenomenology or Theoretical Physics. In addition, theoretical computer simulations can be a delightful tool for studying these topics. Within the area of Quantum Field Theory, I would like to learn more about (the) Renormalization (Group), Effective Field Theories, Parton Distribution Functions and Anomalies, since I came across these topics here and there (some in more detail than others) and those piqued my curiosity. Currently I study these topics by myself to become more familiar with them. Furthermore, I have interest in Physics beyond the Standard Model and its many open problems. To study this area, I have especially interest in learning more about String Theory, to broaden my horizon in combining General Relativity with the Quantum World, and Quantum Gravity.