An operator-theoretical treatment of the Maskawa-Nakajima equation in the massless abelian gluon model
An operator-theoretical treatment of the Maskawa-Nakajima equation in the massless abelian gluon model
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DOI：
10.1016/j.jmaa.2014.04.029
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发表时间：
2014-10-15
影响因子：
1.3
通讯作者：
Watanabe, Shuji
中科院分区：
文献类型：
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作者：
Watanabe, Shuji
Maskawa-Nakajima方程在基本粒子物理学中引起了相当大的兴趣。本文从算符理论的角度研究了无质量交换胶子模型中的Maskawa-Nakajima方程。我们首先证明了当参数λ满足λ> 2时，Maskawa-Nakajima方程存在非零解。此外，我们还证明了该解是无穷可微的且是严格递减的。由此我们得出结论：当λ> 2时，无质量阿贝尔胶子模型自发产生非零夸克质量，并表现出自发的手征对称性破缺。接下来我们证明了当0 < lambda < 1时，Maskawa-Nakajima方程存在唯一的解0，由此我们得出结论，每个夸克保持无质量，并且当0 < lambda < 1时，模型实现了手征对称性。(C)2014爱思唯尔公司All rights reserved.
The Maskawa-Nakajima equation has attracted considerable interest in elementary particle physics. From the viewpoint of operator theory, we study the Maskawa-Nakajima equation in the massless abelian gluon model. We first show that there is a nonzero solution to the Maskawa-Nakajima equation when the parameter lambda satisfies lambda > 2. Moreover, we show that the solution is infinitely differentiable and strictly decreasing. We thus conclude that the massless abelian gluon model generates the nonzero quark mass spontaneously and exhibits the spontaneous chiral symmetry breaking when lambda > 2. We next show that there is a unique solution 0 to the Maskawa-Nakajima equation when 0 < lambda < 1, from which we conclude that each quark remains massless and that the model realizes the chiral symmetry when 0 < lambda < 1. (C) 2014 Elsevier Inc. All rights reserved.