High Precision Calculations in Quantum Field Theory

在过去的几年里，大型强子对撞机（LHC）已经从一个原始的发现转变为一台高精度的机器。尽管很多人都有这样的期望，但到目前为止还没有发现新现象的直接信号，比如额外的空间维度、超对称、低尺度引力等。因此，“新物理学”很可能只是以实验数据与基于粒子相互作用标准模型的理论预测的微小偏差的形式出现。与此同时，低能实验精度的提高使得粒子物理的基本参数得到了非常精确的确定，并在探索超出标准模型的物理方面具有竞争力。因此，能够提供所需精度的理论分析变得至关重要。该项目的主要目的是计算从非相对论性阈值到超相对论性Regge和Sudakov极限等一系列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现象学意义。拟议研究中最有趣的领域之一与大型强子对撞机的希格斯玻色子物理项目有关。它包括通过胶子和电弱规范玻色子聚变产生希格斯玻色子或一对希格斯玻色子的两个主要通道的微扰分析。近二十年来，微扰量子场论的方法和技术达到了前所未有的水平。在量子色动力学中，已经获得了一些关键过程的次-次-次-次-领先的结果，例如大型强子对撞机的Drell-Yan和希格斯玻色子的产生，以及未来线性对撞机的顶夸克-反夸克对阈值的产生。然而，许多悬而未决的问题仍然超出了现有技术的直接计算范围，或者超出了任何有限阶的摄动理论。这些问题需要新的理论和计算工具的发展，这些工具与量子场论的基本概念密切相关，如有效场论方法、重整化群、渐近展开等。更深入地理解和发展这些概念也是该项目的目标之一。运用继承自量子场论的思想已成为现代凝聚态物理学的主要趋势之一。诸如马约拉纳费米子、磁单极子、超对称等在粒子物理基础层面尚未被发现的概念，在各种凝聚态体系中得到了有效的实现。这对量子场论方法在凝聚态物质中的应用具有重要的推动作用。我计划继续研究量子场与凝聚态物质界面处的物理现象，并在此背景下发展和应用先进的微扰方法。

Over the last few years the Large Hadron Collider (LHC) has transformed from a raw discovery into a high-precision machine. Despite many expectations no direct signal of new phenomena such as the extra space dimensions, supersymmetry, low-scale gravity etc. has been detected so far. Thus the "new physics" is likely to show up only as a tiny deviation of the experimental data from the theoretical predictions based on the standard model of particle interactions. At the same time the 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  physics beyond the standard model. Hence, the theoretical analysis which is able to provide the required precision becomes ultimately important.  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 threshold to ultrarelativistic Regge and Sudakov limit, which are of primary phenomenological importance for current and future experiments. One of the most interesting  field of the proposed research is related to the Higgs boson physics program at the LHC. It includes the perturbative analysis of  two main channels for the production of the Higgs boson or a pair of the Higgs bosons via gluon and electroweak gauge boson fusion. During the last two decades the methods and techniques of the perturbative quantum field theory reached an unprecedented level. The next-to-next-to-next-to-leading results have been obtained in quantum chromodynamics  for a number of the key processes such as Drell-Yan and the Higgs boson production at the LHC and the top quark-antiquark pair threshold production at a future linear collider. However, many of the pending problems  are still beyond the reach of available techniques for a direct calculation or go beyond any finite order of perturbation theory. These problems require a development of the new theoretical and computational tools, which are closely related to the fundamental concepts of the quantum field theory such as the effective field theory approach, renormalization group, asymptotic expansions, etc. Deeper understanding and development of these concepts are also among the aims of the project. The use of the ideas inherited from quantum field theory has become one of the main trends in the modern condensed matter physics. Such concepts as Majorana fermions, magnetic monopoles, supersymmetry etc., which are yet to be discovered at fundamental level in particle physics, are effectively realized in various condensed matter systems. This gives a significant boost to the application of the quantum field theory methods to condensed matter. I plan to continue the study of physical phenomena at the interface between the quantum fields and condensed matter and to develop and apply the advanced perturbative methods in this context.