Nonperturbative quantum field theory

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My topic of research is Quantum Field Theory (QFT), the set of equations that describe the electromagnetic, weak, and strong interactions of the elementary particles. QFT is an amazing framework, whose application to Nature led to the discovery of the Higgs particle (hypothesized by theorists 50 years ago) at the Large Hadron Collider in 2012.  Yet, despite the success, many puzzles remain and, at the moment, we are not sure about their solution. For example, we have no clue as to why the masses of the elementary particles span many orders of magnitude, from the lightest neutrinos to the heaviest (so far) top quarks and the Higgs. This is the so-called "mass hierarchy" problem of Nature. A better understanding of the fundamentals of QFT is required (apart from experiment, of course) in order to make progress. However, QFT is also an amazingly complicated set of equations, intractable in most cases. This is true, in particular, for the strong hadronic interactions, responsible for the binding of quarks in protons. Other forms of hypothetical, not yet observed, strong interactions may be responsible for explaining the "mass hierarchy" puzzle.  One focus of my current work is on situations where the set of equations of QFT simplifies enough, so that it can be studied and comprehended intuitively, without the use of big computers, while retaining many of the features important in the real world of hadrons. In this manner, we have gained new insight into the origin of the force holding (or "confining") quarks together, and in particular into the "liberation" of quarks from hadrons upon heating them up, as in the Big Bang or in heavy-ion collisions. It also appears that these studies may help us gain new insight into the deeper mathematical structures underlying QFT. To motivate my second current interest, I already noted that solving the equations of QFT often requires the use of big computers. Big computing has been very successfully applied to the hadronic interactions. However, for the weak interactions (completing, along with electromagnetism, the so-called Standard Model of elementary particles) it is not known how to formulate the equations in a way suitable for computers to use. This may appear strange, but it is a fact, having to do with the so-called "chiral" nature of the weak interactions. I am studying ways to formulate the Standard Model in a way that will make it accessible to computers. If this problem is solved, it may have important future uses for better understanding of the elementary particle interactions at energies higher than the ones currently achievable.