Nonperturbative quantum field theory

我的研究课题是量子场论（QFT），描述基本粒子的电磁，弱和强相互作用的方程组。QFT是一个令人惊叹的框架，它在自然界的应用导致了2012年在大型强子对撞机上发现了希格斯粒子（50年前由理论家假设）。 然而，尽管取得了成功，但仍存在许多难题，目前，我们还不确定它们的解决方案。例如，我们不知道为什么基本粒子的质量跨越了许多数量级，从最轻的中微子到最重的顶夸克和希格斯玻色子。这就是自然界所谓的“质量等级”问题。为了取得进展，需要更好地理解QFT的基本原理（当然，除了实验）。然而，QFT也是一组令人惊讶的复杂方程，在大多数情况下难以处理。特别是对于强强子相互作用来说，这是正确的，强强子相互作用是夸克与质子结合的原因。其他形式的假设，尚未观察到的，强相互作用可能是解释“质量等级”之谜的原因。 我目前工作的重点之一是研究QFT方程组足够简化的情况，这样就可以直观地研究和理解它，而不需要使用大型计算机，同时保留了强子真实的世界中的许多重要特征。通过这种方式，我们对将夸克束缚在一起的力的起源有了新的认识，特别是对加热强子时夸克从强子中“解放”的认识，如在大爆炸或重离子碰撞中。这些研究也可能帮助我们对QFT背后更深层次的数学结构有新的认识。 为了激发我当前的第二个兴趣，我已经注意到，求解QFT方程通常需要使用大型计算机。大计算已经非常成功地应用于强子相互作用。然而，对于弱相互作用（沿着电磁作用，即所谓的基本粒子标准模型），我们还不知道如何以适合计算机使用的方式来表达方程。这可能看起来很奇怪，但这是一个事实，与弱相互作用的所谓“手征”性质有关。我正在研究如何以一种计算机可以访问的方式来制定标准模型。如果这个问题得到解决，它可能有重要的未来用途，以更好地理解能量高于目前可实现的基本粒子相互作用。

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.