Dynamical Breaking of Chiral Symmetry

本研究的目的是寻找手性对称性自发破缺的机制。有效势为研究自发对称性破缺提供了最有效的工具。然而，很难找到像psisi这样的局部复合算子的有效潜力。通过对Nambu-Jona-Lasinio模型的研究，提出了一种通过考虑Higg标量场和强相互作用的影响来定义这类局部复合算符的明确有效势的新方法，并从Nambu-Jona-Lasinio模型中提取了导致手征对称性自发破缺的机制.当无质量夸克和反夸克之间的引力变得足够强时，在最具吸引力的通道中出现束束态。这种束缚状态不可避免地是一个快子，因为组成粒子的粒子是无质量的，真空变得不稳定。为了治愈这种不稳定性，真空会重新安排自己，赋予夸克适当的质量，使束缚态成为稳定的无质量玻色子。这一基本机制是普遍的，与特定的模型无关。事实上，我们已经证明了QCD中的手征对称性是通过这种机制自发破缺的。为此，在Schwinger-Dyson方程中引入QCD的渐近自由性质，以获得非平凡的连续极限是必不可少的。

The aim of this research is to find the mechanism of the spontaneous breaking of chiral symmetry. Effective potential offer the most efficient tool to study spontaneous symmetry breaking. It has been difficult, however, to find the effective potential for local composite operators such as psipsi. A new method is proposed to define the unambiguous effective potential for such local composite operators by taking into account the effects of the Higg's scalar fields together with those of the strong interactions.The mechanism causing the spontaneous breaking of chiral symmetry is extracted from the study of the Nambu-Jona-Lasinio model. When the attractive force between massless quarks and anti-quarks becomes strong enough, a bound state appears in the most attractive channel. This bound state is inevitably a tachyon since the constituent particles are massless, and the vacuum becomes unstable. In order to cure this instability the vacuum rearranges itself to give appropriate mass to the quarks so that the bound state becomes a stable massless boson.This fundamental mechanism is universal and independent of specific models. In fact, we have shown the chiral symmetry breaks down spontaneously by this mechanism in QCD. In so doing it is essential to incorporate the asymptotic free property of the QCD in the Schwinger-Dyson equation in order to obtain the non-trivial continuum limit.