论文标题
连续体和晶格中重新归一化组变换的新方法
Novel Approaches to Renormalization Group Transformations in the Continuum and on the Lattice
论文作者
论文摘要
该论文是关于在连续时空背景和晶格离散化中实现RG转换的新方法。从欧几里得量子场理论的角度探讨了该主题。作为基于晶格模拟的计算方法的论文，我强调了整个工作中晶格制剂的作用，尤其是在前两章中。首先，我描述了晶格理论的基本方面及其与RG的共生。在第二个中，我基于一种称为梯度流（GF）的数值工具，提出了一种新的，连续的RG方法。将提出来自2和3维度（$ ϕ^4_d $）的四分位标量场理论的仿真结果，将提出4维12FAIRAVIAL SU（3）量规理论。在第三章和第四章中，重点变得更加分析。第3章是功能重归其化组（FRG）的介绍性综述。在第4章中，我通过研究FRG和随机过程之间的关系介绍了随机RG（SRG）的概念。
This thesis is about new methods of achieving RG transformations, in both a continuum spacetime background and on a lattice discretization thereof. The subject is explored from the point of view of euclidean quantum field theory. As a thesis grounded on the computational method of lattice simulation, I emphasize the role of lattice formulations throughout the work, especially in the first two chapters. In the first, I describe the essential aspects of lattice theory and its symbiosis with RG. In the second, I present a new, continuous approach to RG on the lattice, based on a numerical tool called Gradient Flow (GF). Simulation results from quartic scalar field theory in 2 and 3 dimensions ($ϕ^4_d$) and 4-dimensional 12-flavor SU(3) gauge theory will be presented. In the third and fourth chapters, the focus becomes more analytic. Chapter 3 is an introductory review of Functional Renormalization Group (FRG). In chapter 4, I introduce the concept of Stochastic RG (SRG) by working out the relationship between FRG and stochastic processes.
