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arXiv 0709.0161hep-ph
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QCD中规范不变夸克两点格林函数的积分方程

Integral equation for gauge invariant quark two-point Green's function in QCD

H. Sazdjian

摘要:

考虑了用路径有序胶子场相因子沿连接夸克和反夸克的斜折线定义的规范不变夸克两点格林函数。建立了不同路径段数的格林函数之间的函数关系。一个积分方程获得的格林函数定义的相位因子沿一条直线。该方程涉及一个无限系列的两点格林函数,具有越来越多的路径段;相关的内核涉及威尔逊圈与轮廓对应的斜多边形线的陪同格林函数和功能的衍生物沿轮廓的两侧。该级数可以看作是威尔逊圈的泛函导数的整体数的展开。最低阶的内核,其中涉及一个威尔逊圈与两个功能的衍生物,提供了一个近似的解决方案的方程的框架。

英文摘要:

Gauge invariant quark two-point Green's functions defined with path-ordered gluon field phase factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green's functions with different numbers of path segments are established. An integral equation is obtained for the Green's function defined with a phase factor along a single straight line. The equation implicates an infinite series of two-point Green's functions, having an increasing number of path segments; the related kernels involve Wilson loops with contours corresponding to the skew-polygonal lines of the accompanying Green's function and with functional derivatives along the sides of the contours. The series can be viewed as an expansion in terms of the global number of the functional derivatives of the Wilson loops. The lowest-order kernel, which involves a Wilson loop with two functional derivatives, provides the framework for an approximate resolution of the equation.

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