论文标题
在路径综合语言中解决能量密度函数I：应用于（0+0）-d $ O（n）$ - 对称$φ^{4} $的图形技术的比较研究
Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric $φ^{4}$-theory
论文作者
论文摘要
能量密度功能（EDF）方法当前是唯一能够应对整个核图表的微观理论方法。然而，它受到其经验特征造成的限制，并恶化了其可靠性。本文是一个较大计划的一部分，旨在将EDF方法作为有效的现场理论（EFT）制定，以克服这些局限性。实现此目的的相关框架是量子场理论（QFT）的路径综合（PI）公式。后者确实提供了多种多体问题的多种处理方法，非常适合处理非扰动互动，并利用EFT作为起点而产生的Lagrangian。在一般环境中开发形式主义的同时，我们介绍了应用于玩具模型的此类技术的比较研究，即（0+0）-d $ o（n）$ - 对称$φ^{4} $ - 理论。更具体地说，我们的重点将放在以下图解技术上：环路扩展（LE），优化的扰动理论（OPT）和自洽扰动理论（SCPT）。通过这些方法，我们特别注意$ O（n）$对称的自发分解，特别是因为自发对称性断裂（SSB）在EDF方法的当前实现中起着至关重要的作用。
The energy density functional (EDF) method is currently the only microscopic theoretical approach able to tackle the entire nuclear chart. Nevertheless, it suffers from limitations resulting from its empirical character and deteriorating its reliability. This paper is part of a larger program that aims at formulating the EDF approach as an effective field theory (EFT) in order to overcome these limitations. A relevant framework to achieve this is the path-integral (PI) formulation of quantum field theory (QFT). The latter indeed provides a wide variety of treatments of the many-body problem well suited to deal with non-perturbative interactions and to exploit a Lagrangian resulting from an EFT as a starting point. While developing the formalism in a general setting, we present a comparative study of such techniques applied to a toy model, i.e. the (0+0)-D $O(N)$-symmetric $φ^{4}$-theory. More specifically, our focus will be on the following diagrammatic techniques: loop expansion (LE), optimized perturbation theory (OPT) and self-consistent perturbation theory (SCPT). With these methods, we notably address the spontaneous breakdown of the $O(N)$ symmetry with care especially since spontaneous symmetry breakings (SSBs) play a paramount role in current implementations of the EDF approach.
