论文标题
在路径综合语言中解决能量密度函数II：应用于（0+0）-d $ O（n）$ - 对称$φ^{4} $的功能重新归一化组技术的比较研究
Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric $φ^{4}$-theory
论文作者
论文摘要
本文是一系列出版物的第二本，旨在研究相关方向，以将核能密度功能（EDF）方法作为有效的田间理论（EFT）转变。 EDF方法在过去几十年中已经知道了核理论的许多成功，目前是唯一可以应用于所有原子核的微观技术。但是，EDF方法的现象学特征也具有重要的局限性，例如缺乏与量子染色体动力学（QCD）的明确联系。正如本系列的第一篇论文所说的那样，将EDF框架重新设计为EFT将使我们能够克服这些局限性。特别是，路径综合（PI）技术适合实现其目的，因为它们允许设计多种非扰动近似值，并且可以将Lagrangians可能从QCD的EFT衍生而来，作为输入。在我们之前的论文中，我们在研究（0+0）-d $ O（n）$ - 对称$φ^{4} $ - 理论的研究中说明了图解PI技术的这种技术特征。在目前的工作中，我们考虑了另一种类别的PI技术，即功能重归其化组（FRG）方法，我们适用于同一玩具模型。 Despite our explicit interest for the nuclear many-body problem, the presented study is also directed towards FRG practitioners from various fields: technical details are provided for FRG techniques based on 1-particle-irreducible (1PI), 2-particle-irreducible (2PI) and 2-particle-point-irreducible (2PPI) effective actions (EAs), coined respectively as 1PI-, 2PI- and 2PPI-FRGs, $ O（n）$对称的处理也得到了彻底解决。这些各种FRG方法之间的连接也被确定。
The present paper is the second of a series of publications that aim at investigating relevant directions to turn the nuclear energy density functional (EDF) method as an effective field theory (EFT). The EDF approach has known numerous successes in nuclear theory over the past decades and is currently the only microscopic technique that can be applied to all atomic nuclei. However, the phenomenological character of the EDF method also comes with important limitations, such as the lack of an explicit connection with quantum chromodynamics (QCD). As was argued in the first paper of this series, reformulating the EDF framework as an EFT would enable us to overcome these limitations. In particular, path-integral (PI) techniques are suited to achieve such a purpose as they allow to design numerous non-perturbative approximations and can take Lagrangians possibly derived from EFTs of QCD as inputs. In our previous paper, we have illustrated such technical features for diagrammatic PI techniques in a study of the (0+0)-D $O(N)$-symmetric $φ^{4}$-theory. In the present work, we consider another class of PI techniques, i.e. functional renormalization group (FRG) approaches, that we apply to the same toy model. Despite our explicit interest for the nuclear many-body problem, the presented study is also directed towards FRG practitioners from various fields: technical details are provided for FRG techniques based on 1-particle-irreducible (1PI), 2-particle-irreducible (2PI) and 2-particle-point-irreducible (2PPI) effective actions (EAs), coined respectively as 1PI-, 2PI- and 2PPI-FRGs, and the treatment of the $O(N)$ symmetry is also addressed thoroughly. Connections between these various FRG methods are identified as well.
