High precision calculations in quantum field theory

接下来的十年对我们理解基本粒子和力的基本结构至关重要。大型强子对撞机Run 2已经以前所未有的13 TeV的质心能量采集数据，这可能在不久的将来发现主要的新现象，如额外的空间维度，超对称等。另一方面，低能实验精度的提高使粒子物理的基本参数得到非常精确的确定，并在探索超越粒子相互作用标准模型的新物理方面具有竞争力。在大多数情况下，新物理学可能会表现为与基于标准模型的理论预测的微小偏差。因此，预测的高精度就变得必不可少了。***本项目的主要目的是计算从非相对论性到超相对论性极限的广泛量子场论问题中的高阶微扰修正，这对当前和未来的实验具有重要的现象学意义。研究结果对于研究电弱对称性破缺和费米子质量产生等基本现象，精确确定重夸克质量和强耦合常数等粒子物理基本参数具有重要意义。量子电动力学中类氢束缚态的高阶分析给出了物理学中最准确的预测之一，即将面对正在进行的实验结果，并可能为“奇异的”新物理学（如镜像宇宙、大额外维度和电荷粒子）提供最敏感的测试之一。***所提出问题的难度要求开发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。***量子场论的许多思想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界面的物理现象。特别是，在计量学中起着重要作用的单电子隧穿装置的电流标准精度的确定，场论方法可能是至关重要的

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.**