QCD中的非微扰Dyson--Schwinger方程：一种初步近似
Nonperturbative Dyson--Schwinger equations in QCD: a first approximation
浏览论文内容
中文总结 AI 辅助
本文提出一种基于无限非微扰Dyson-Schwinger方程系统的截断近似方案，通过标量场因子化、自由度划分及格林函数近似等方法实现非微扰量子化，并探讨了质量间隙、维度嬗变及其与湍流理论的类比。
中文摘要 AI 辅助
我们考虑一种基于无限非微扰Dyson--Schwinger方程系统的非微扰量子化程序。我们提出了一种在静态情形下截断这一无限方程系统的初步近似。该近似所依据的主要思想如下：（a）通过引入标量场，将真空规范场的两点格林函数因子化；（b）在非真空情形下，$SU(3)$规范场的自由度可分为“几乎经典”和“几乎量子”两类自由度；（c）规范场的四点格林函数表示为两点格林函数的双线性组合；（d）提出了一种描述夸克与规范场之间相互作用的三点格林函数的近似，该近似导致原始夸克场算符的Dirac方程分裂为两个方程，一个描述费米子场的期望值，另一个则获得非线性项并用于描述由真空规范场束缚的海夸克所构成的凝聚体。我们考虑了适用于这一非微扰量子化近似的规范选择。我们指出，在该近似中出现的非线性Dirac方程可能导致相应方程系统解的能量谱中出现质量间隙。本文还讨论了在该近似中出现“维度嬗变”的问题。我们提供了支持以下观点的论据：在有限截断中出现并导致“维度嬗变”的“闭合常数”在过渡到无限Dyson--Schwinger方程系统时应当保留。此外，还讨论了非微扰量子化与湍流随机理论之间的类比。
英文摘要
We consider a procedure for nonperturbative quantization based on an infinite system of nonperturbative Dyson--Schwinger equations. We propose a first approximation for truncating this infinite system of equations in the static case. The main ideas underlying this approximation are as follows: (a) the two-point Green's functions of vacuum gauge fields are factorized by introducing scalar fields; (b) in the non-vacuum case, the degrees of freedom of the $SU(3)$ gauge field can be divided into ``almost classical'' and ``almost quantum'' degrees of freedom; (c) the four-point Green's functions of the gauge fields are represented as bilinear combinations of two-point Green's functions; (d) an approximation for the three-point Green's function describing the interaction between quarks and gauge fields is proposed, which leads to the splitting of the original Dirac equation for the quark-field operators into two equations, one describing the expectation value of the fermion field and the other acquiring a nonlinear term and serving to describe a condensate composed of sea quarks bound by the vacuum gauge field. We consider the choice of gauge appropriate for this approximation to nonperturbative quantization. We point out that the emergence of a nonlinear Dirac equation within this approximation may lead to a mass gap in the energy spectrum of solutions of the corresponding systems of equations. The issue of the emergence of ``dimensional transmutation'' within this approximation is also discussed. We provide arguments in favor of the statement that the ``closure constants'' appearing in the finite truncation and giving rise to ``dimensional transmutation'' should survive in the transition to the infinite system of Dyson--Schwinger equations. An analogy between nonperturbative quantization and the stochastic theory of turbulence is also discussed.
发表机构
- Farabi University（法拉比大学）
- Academician J. Jeenbaev Institute of Physics of the NAS of the Kyrgyz Republic（吉尔吉斯共和国国家科学院J. Jeenbaev院士物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
