Nonperturbative dynamics in the standard model and beyond

标准模型(SM)是研究强相互作用和弱电相互作用的场论框架。该理论中尚未解决的主要问题[如电弱对称破缺机制、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]要么与量子场论中未知的或鲜为人知的非微扰动力学有关。本项目将致力于以下三个方向的非微扰动力学研究。A)相对论致密物质的动力学：预计致密(但不是很热)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，有更多的动机来研究致密相对论物质的性质，无论有没有磁场，都是如此，非常详细。B)电弱对称破缺和费米子质量：电弱对称破缺与另一个基本问题--夸克和轻子的质量谱密切相关。由于这些问题将是大型强子对撞机(CERN)实验研究的中心问题，它们具有重大的理论和现象学价值。我正在计划开发一种方法，在这种方法中，顶夸克和复合希格斯玻色子的动力学发挥着核心作用。C)量子场理论方法在凝聚态系统中的应用：值得注意的是，相对论场论能够在高温超导体和碳基材料，特别是石墨烯这一单原子层的石墨烯等凝聚态系统中作为有效的理论。由于这些材料潜在的卓有成效的应用，它们的重要性怎么估计都不为过。我计划继续利用量子场论中发展的先进方法来研究凝聚态系统。重点将是研究石墨烯及其由两个紧密相连的石墨烯层组成的双层“表亲”的动力学。后者在高科技应用方面具有巨大的潜力。

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.