Projects
Projects
In this term project, I studied gauge theories in the language of differential forms and fiber bundle technology. The emphasis was on the Yang-Mills theory and its instantons. I tried to show how this geometric interpretation and their implications in quantum field theory is useful. First, differential forms are briefly introduced. Then, we studied the U(1) gauge theory as an simple example. From there we focused on SU(2) gauge theory and its instantons.
For my senior year project, I am studying with Dr. Ahmet Keleş. The aim of the project is to understand the applications of lattice gauge theories and spin systems in condensed matter systems. To this end, we also study Kitaev's toric code which is at the heart of the modern fault-tolerant quantum computing models. The project is still ongoing.
This project was for a graduate course PHYS777: Bootstrap Methods in Theoretical Physics. I thoroughly studied Scale Invariance vs. Conformal Invariance in various disciplines such as statistical mechanics, quantum field theory and string theory. In this regard, I analyzed most of the seminal papers in the field, wrote a review report on the subject and presented it. The seemingly simple idea of when and how scale invariance implies conformal invariance has turned out to be a very deep and non-trivial subject. In this project, I experienced the renormalization group methods, conformal bootstrap and consequences of this implication in different areas of theoretical physics.