High precision calculations in quantum field theory

接下来的十年对于我们理解基本粒子和力的基本结构是至关重要的。大型强子对撞机RUN 2已经在以前所未有的13TeV的质心能量获取数据，这可能在不久的将来主要发现新的现象，如额外的空间维度、超对称性等。另一方面，低能量实验的日益精确使得能够非常准确地确定粒子物理的基本参数，并在探索超越粒子相互作用标准模型的新物理方面变得有竞争力。在大多数情况下，新物理学可能会表现出与基于标准模型的理论预测的微小偏差。因此，预测的高精度成为强制性的。 该项目的主要目的是计算从非相对论到超相对论极限的一大类量子场论问题中的高阶微扰修正，这些问题对当前和未来的实验具有重要的唯象意义。拟议的研究结果对于研究基本现象，如电弱对称破缺和费米子质量产生，对于精确确定粒子物理的基本参数，如重夸克质量和强耦合常数等，是至关重要的。量子电动力学中对类氢束缚态的高阶分析给出了与正在进行的实验结果相对抗的物理学中最准确的预测之一，并可能提供对镜像宇宙、大额外维度和毫克粒子等“奇异”新物理最敏感的测试之一。 这些问题的困难需要发展新的理论和计算工具，这些工具与量子场论的基本概念密切相关，包括有效场论方法、重整化群、不稳定粒子产生和晶格规范理论。更深入地理解和发展这些概念也是该项目的目标之一。 量子场论的许多观点在现代凝聚态物理中也被证明是非常有用的。我计划继续研究这些领域之间交界处的物理现象。特别是，场论方法对于确定基于单电子隧道器件的电流标准的准确性至关重要，因为单电子隧道器件在计量学中起着重要的作用。

The following decade is crucial for our understanding of the fundamental structure of elementary particles and forces. The Large Hadron Collider Run 2 is already taking data at unprecedented center-of-mass energy of 13 TeV, which could in a nearest future uncover principally new phenomena such as the extra space dimensions, supersymmetry, etc. On the other hand increasing accuracy of the low-energy experiments allows for a very accurate determination of the fundamental parameters of particle physics and becomes competitive in probing new physics beyond the standard model of particle interactions. In most cases the new physics may show up as a tiny deviation from the theoretical predictions based on the standard model. Thus the high precision of the predictions becomes mandatory. The main aim of the project is the calculation of the high-order perturbative corrections in a wide class of the quantum field theory problems ranging from nonrelativistic to ultrarelativistic limit, which are of primary phenomenological importance for current and future experiments. The results of the proposed research are crucial for the study of the fundamental phenomena such as the electroweak symmetry breaking and the fermion mass generation, for precise determination of the fundamental parameters of particle physics such as the heavy quark masses and the strong coupling constant, etc. The high-order analysis of the hydrogen-like bound states within quantum electrodynamics gives one of the most accurate predictions in physics to be confronted with the results of the ongoing experiments, and may provide one of the most sensitive tests of an "exotic" new physics such as the mirror universe, large extra dimensions and millicharge particles. The difficulty of the suggested problems requires developing new theoretical and computational tools, which are closely related to the fundamental concepts of the quantum field theory including the effective field theory approach, renormalization group, unstable particle production and lattice gauge theories. Deeper understanding and development of these concepts are also among the aims of the project. Many ideas of quantum field theory proved to be very useful also in modern condensed matter physics. I plan to continue the study of physical phenomena at the interface between these fields. In particular, the field theoretical methods may be crucial for determination of the accuracy of the electric current standards based on the single-electron tunneling devices, which play an important role in metrology.