Relativistic Quantum Mechanics
Two of the great revolutions of physics in the 20th century were relativity and quantum mechanics. Combining special relativity and quantum mechanics produced relativistic quantum mechanics or, as it is better known, quantum field theory. As soon as it was created, quantum field theory predicted the existence of antiparticles which were discovered shortly afterwards. Almost a century later, quantum field theory has become a mature field and is the framework within which the Standard Model of particle physics is built. The Standard Model has been extremely successful at predicting and explaining almost all experiments to date, with the most recent success being the spectacular confirmation of the Higgs boson predicted by the Standard Model. Nevertheless, there are many outstanding problems that are not yet accounted for by the Standard Model. Among those are the fine-tuning problem of the Higgs boson, the properties of dark matter, the explanation for dark energy, a detailed understanding of the hierarchy of fermion masses and the abundance of matter but not antimatter in the universe. On the other hand, there are also fundamental problems with quantum field theory itself. It is not able to successfully accommodate gravity at very small scales and therefore appears to be incomplete. Furthermore, new methods of calculating the probability of particle scattering appear to be leading us towards a more fundamental theory of relativistic quantum mechanics opening up new areas of research into fundamental physics.
My research deals with the exploration of these problems, both in the Standard Model and in the fundamental aspects of relativistic quantum mechanics itself. I use a combination of analytical and computational methods to explore these problems, sometimes emphasizing one and sometimes the other. Computational power continues to grow exponentially, following Moore's law, enabling ever more complex calculations. It is my belief that this will create one of the next revolutions in fundamental physics and therefore apply a good amount of my time in this direction. On the other hand, a new theoretical understanding of a problem can often far surpass even the most powerful computational model. So, I think it is important to approach fundamental physics from both directions and find the most advantageous route at a particular time. Here are a few of my recent publications:
On Tree-Level Unitarity in Theories of Massive Spin-2 Bosons NDC and Stefanus (a graduate student at the University of PIttsburgh) We analyzed the scattering of massive spin-2 bosons in a theory with generic couplings in order to determine whether conservation of probability could be achieved at "tree-level". We wrote a computational code to calculate these complicated scattering amplitudes and analyze whether the probability conservation could be achieved in each case.
A New Method for the Spin Determination of Dark Matter NDC and Daniel Salmon (an undergraduate at the University of Pittsburgh) We developed and simulated the use of a new analytical formula to determine the spin of dark matter at an electron-positron collider that is planned to be built in the near future. We wrote computational code and ran extensive simulations of particle collisions to show the efficacy of our new formula for determining the dark matter spin.
FeynRules 2.0 - A Complete Toolbox for Tree-Level Phenomenology Adam Alloul, NDC, Celine Degrande, Claude Duhr and Benjamin Fuks We released version 2.0 of a computational physics code that we wrote that enables physicists to implement and study new theoretical models that attempt to explain the challenges with the Standard Model described above. This is an update of version 1.0 which was authored by myself and Claude Duhr (who was a graduate student at the time) and has been extremely popular in our field.
A complete listing of my publications can be found on the inSpire website.