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arXiv 1106.0691hep-phhep-lathep-th
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库仑规范量子色动力学的夸克扇区

Quark sector of Coulomb gauge Quantum Chromodynamics

Carina Popovici

摘要:

用泛函积分方法研究了库仑规范量子色动力学的夸克部分。导出了夸克对Dyson-Schwinger方程的贡献,给出了两点函数的单圈微扰结果。在重夸克极限下,通过重夸克质量展开重写量子色动力学的生成泛函,解决了禁闭问题。通过限制在这个扩展的领导顺序,并考虑只有两个点的功能的杨米尔斯部门,彩虹阶梯近似的间隙和Bethe-Salpeter方程是准确的。在夸克间距相等的情况下,给出了夸克-反夸克束缚态的Bethe-Salpeter方程和三夸克束缚态的Faddeev方程的非微扰解析解.导出了夸克-反夸克和三夸克禁闭势,发现时间胶子传播子与相应的弦张力之间有直接联系,指出物理上只允许夸克-反夸克(介子)和qqq(重子)态的色单态.此外,四点格林函数,在夸克-反夸克和双夸克通道,明确地推导。结果表明,相应的极点与重夸克系统的束缚态能量有关,格林函数的物理极点与非物理极点自然分离。

英文摘要:

The quark sector of Coulomb gauge quantum chromodynamics is considered within the functional integral approach. The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point functions are presented. The problem of confinement is addressed in the heavy quark limit, by rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion. By restricting to leading order in this expansion and considering only the two-point functions of the Yang-Mills sector, the rainbow-ladder approximation to the gap and Bethe-Salpeter equations is shown to be exact. Analytic nonperturbative solutions to the Bethe-Salpeter equation for quark-antiquark bound states and Faddeev equation for three-quark bound states, in the case of equal quark separations, are presented. The quark-antiquark and three-quark confining potentials are derived and a direct connection between the temporal gluon propagator and the corresponding string tensions is found. It is shown that only color singlet of quark-antiquark (meson) and qqq (baryon) states are physically allowed. Moreover, the four-point Green's functions, in both quark-antiquark and diquark channels, are explicitly derived. It is found that the corresponding poles relate to the bound state energy of the heavy quark systems, and a natural separation between physical and unphysical poles in the Green's functions emerges.

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