Scale Invariance in Quantum Field Theory

该奖项资助肯塔基大学阿纳托利·戴马斯基教授的研究活动。提出的研究计划涉及量子场论，这是描述基本粒子动力学的通用理论框架。在众多不同的场论模型中，有一些更简单、更基本，并且不包括量纲参数。这个项目的目标是通过发展新的理论方法，不依赖于基本粒子之间的相互作用是弱的假设，来推进我们目前对这种没有内部尺度的量子场论的理解。所得结果将用于进一步阐明连续系统达到平衡的机制。因此，该项目通过扩展我们目前在量子场论基本特性领域的基础科学知识，服务于国家利益，量子场论在许多科学领域都有应用。预计该项目还将产生更广泛的重大影响。该项目的目标之一是通过研究生和年轻研究人员的参与来提高研究生和研究生物理教育的质量。此外，这项研究将有助于我们在基础层面上对自然的理解，这是公众感兴趣的。PI还通过公开演讲和与一组电影制片人合作制作一部普及现代物理学的科幻电视剧，积极致力于推广基本粒子物理学。在更技术性的层面上，这个项目的目标是研究没有内部尺度的量子场论。对尺度不变模型的关注是合理的，因为扩展的对称性提供了额外的理论控制，以及这些模型在通过适当选择的变形定义其他理论时发挥的基本作用。该项目的具体目标可分为三大类：研究量子场论中尺度与共形不变性之间的联系，识别尺度不变非共形场论的特征性质；在量子场论系统中发展热化理论，特别是将本征态热化假设扩展到连续系统；提高我们对共形场论的普遍性质的理解。这些目标将通过全息对应、共形自举和量子信息理论等非摄动方法的结合来实现。

This award funds the research activities of Professor Anatoly Dymarsky at the University of Kentucky.The proposed research program concerns quantum field theory, the universal theoretical framework for describing the dynamics of the elementary particles. Among the multitude of different field-theoretic models there are those which are simpler, more fundamental, and which include no dimensionful parameters. The goal of this project is to advance our current understanding of such quantum field theories without internal scales by developing new theoretical approaches that do not rely on the assumption that the interactions between the elementary particles are weak. The results obtained will be used to further clarify the mechanism by which continuous systems reach equilibrium. Thus, this project serves the national interest by extending our current knowledge of fundamental science in areas pertaining to basic properties of quantum field theory, which has application across many fields of science. This project is also envisioned to have significant broader impacts. One of the goals of this project is to enhance the quality of graduate and post-graduate physics education through the involvement of graduate students and young researchers. Furthermore, this research will contribute toward our understanding of nature at the fundamental level, which is of interest to the general public. The PI is also actively engaged in promoting elementary-particle physics by giving public lectures and working together with a group of film producers developing a science-fiction TV series popularizing modern physics.On a more technical level, the goal of this project is to study quantum field theories without internal scales. The focus on scale-invariant models is justified by an extended symmetry providing additional theoretical control as well as the fundamental role these models play in defining other theories through appropriately chosen deformations. The specific aims of the project can be divided into three broad categories: to investigate the connection between scale and conformal invariance in quantum field theory and identify characteristic properties of scale-invariant non-conformal field theories; to develop a theory of thermalization in the context of quantum field-theoretic systems, and in particular to extend the Eigenstate Thermalization Hypothesis to continuous systems; and to improve our understanding of the universal properties of conformal field theories. These objectives will be achieved by a combination of non-perturbative methods such as the holographic correspondence, conformal bootstrap, and methods of quantum information theory.