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至关重要。大型强子对撞机运行2已经在以前所未有的13 TeV的质心能量获取数据，这可能在不久的将来主要揭示新的现象，如额外的空间维度，超对称性，另一方面，提高低-能量实验允许非常精确地确定粒子物理学的基本参数，并在探索新物理学方面具有竞争力。粒子相互作用的标准模型在大多数情况下，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各种量子场论问题的高阶微扰修正，这些问题对当前和未来的实验具有重要的唯象意义。拟议研究的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学基本参数，氢的高阶分析-就像量子电动力学中的束缚态给出了物理学中最准确的预测之一，以面对正在进行的实验的结果，并可能提供一个最敏感的测试“外来”的新物理学，如镜像宇宙，大额外维度和毫荷粒子。 所提出的问题的难度需要开发新的理论和计算工具，这是密切相关的量子场论的基本概念，包括有效场论方法，重整化群，不稳定粒子的产生和格点规范理论。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学中也被证明是非常有用的。 我计划继续研究这些领域之间的物理现象。特别是，场理论方法可能是至关重要的确定的准确性的电流标准的基础上的单电子隧穿器件，这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.