We investigate the equal-time (static) quark propagator in Coulomb gauge within the Hamiltonian approach to QCD in d = 2 spatial dimensions. Although the underlying Clifford algebra is very different from its counterpart in d = 3, the gap equation for the dynamical mass function has the same form. The additional vector kernel which was introduced in d = 3 to cancel the linear divergence of the gap equation and to preserve multiplicative renormalizability of the quark propagator makes the gap equation free of divergences also in d = 2.

中文翻译：

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在库仑量规的哈密顿量方法中，QCD 3中的动态夸克质量生成

我们在d = 2空间维度的汉密尔顿方法QCD中研究库仑规中的等时（静态）夸克繁殖体。尽管下面的Clifford代数与d = 3中的对应代数有很大不同，但动力学质量函数的间隙方程具有相同的形式。在d = 3中引入的附加矢量核可消除间隙方程的线性散度并保留夸克传播子的乘法可归一化性，从而使间隙方程在d = 2中也无散度。