Nonperturbative dynamics in the standard model and beyond

标准模型（SM）是强相互作用和电弱相互作用的场论框架。这个理论中主要未解决的问题[如电弱对称性破缺的机制、夸克和轻子的质量谱、量子色动力学（QCD）中的禁闭动力学以及有限温度和重子密度下的QCD动力学]与量子场论中仍然未知或知之甚少的非微扰动力学有关。本计画将致力于下列三个方向的非微扰动力学研究。a）相对论性致密物质的动力学：人们预期致密（且不是很热）的夸克物质可以存在于致密恒星的核心，其中许多恒星具有非常强的磁场。因此，有额外的动机来研究致密相对论性物质的性质，包括有磁场和没有磁场的情况。B）电弱对称性破缺和费米子质量：电弱对称性破缺与另一个基本问题--夸克和轻子的质量谱--密切相关。这些问题将是大型强子对撞机（CERN）实验研究的中心课题，具有重要的理论和唯象价值。我正计划开发一种方法，在这种方法中，顶夸克和复合希格斯玻色子的动力学起着核心作用。c）量子场论方法在凝聚态系统中的应用：相对论场论可以作为高温超导体和碳基材料等凝聚态系统的有效理论，特别是石墨烯，石墨的单原子层。由于这些材料的潜在的富有成效的应用，他们的重要性怎么估计都不过分。我计划继续使用量子场论中开发的先进方法研究凝聚态系统。重点将是研究石墨烯及其双层“表亲”的动力学，双层“表亲”由两个紧密连接的石墨烯层组成。后者具有巨大的高科技应用潜力。

The Standard Model (SM) is the field theoretical framework for strong and electroweak interactions. The main unresolved problems in this theory [such as the mechanism of electroweak symmetry breaking, the mass spectrum of quarks and leptons, the confinement dynamics in quantum chromodynamics (QCD), and QCD dynamics at finite temperature and baryon density] are connected either with still unknown or poorly understood nonperturbative dynamics in quantum field theory. This project will be devoted to studies of nonperturbative dynamics in the following three directions. a) Dynamics in Relativistic Dense matter: It is expected that dense (and not very hot) quark matter can exist in the core of compact stars many of which possess very strong magnetic fields. Consequently, there is additional motivation to study the properties of dense relativistic matter, both with and without magnetic field, in full detail. b) Electroweak Symmetry Breaking and Fermion Masses: Electroweak symmetry breaking is intimately connected with another fundamental problem, the spectrum of mass of quarks and leptons. Since these problems will be the central quest in experimental studies at Large Hadron Collider (CERN), they are of the great theoretical and phenomenological value. I am planning to develop the approach in which the dynamics of the top quark and composite Higgs bosons play the central role. c) Applications of Quantum Field Theoretical Methods in Condensed Matter Systems: It is quite remarkable that relativistic field theories can serve as effective theories in such condensed matter systems as high-temperature superconductors and carbon-based materials, in particular, graphene, a single atomic layer of graphite. Because of potentially fruitful applications of these materials, their importance can be hardly overestimated. I am planning to continue the studies of condensed matter systems by using advanced methods developed in quantum field theory. The emphasis will be on studying the dynamics of graphene and its bilayer ``cousin", consisting of two closely connected graphene layers. The latter has a great potential for high-tech applications.