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arXiv 1207.5950hep-thhep-lathep-ph
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随机量子化和有效action形式中的两个红外Yang-Mills解

Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism

Felipe J. Llanes-Estrada, Richard Williams

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13 pages, 7 figures. Change of title to reflect version accepted for publication
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摘要：

对纯杨-米尔斯理论的量子场方程进行了30年的研究，提炼出了朗道规范下的两类解。这两个解在高（欧几里德）动量时都与已知的微扰理论相吻合，并且都预言了一个红外抑制的横胶子传播子，但是被称为“标度”的解的特点是胶子和鬼传播子的红外幂律，而“质量”解则把胶子描述为一个具有有限德拜屏蔽质量的矢量玻色子。在这项工作中，我们研究这些解决方案的规范依赖，采用随机量子化。我们发现，在四维和彩虹近似下，随机量子化支持朗道规范中的两种解，但当控制漂移力的参数与零分离（软规范固定）时，标度解突然消失，只恢复微扰传播子;大质量解似乎在朗道规范外的扩展中幸存下来。这些结果是一致的标度解与存在的Gribov视界，与大规模的更一般。我们还研究了产生彩虹的Faddeev-Popov量子化的有效作用，并且我们发现，对于裸顶点近似，该量子有效作用的最小化的解决方案。

英文摘要：

Three decades of work on the quantum field equations of pure Yang-Mills theory have distilled two families of solutions in Landau gauge. Both coincide for high (Euclidean) momentum with known perturbation theory, and both predict an infrared suppressed transverse gluon propagator, but whereas the solution known as "scaling" features an infrared power law for the gluon and ghost propagators, the "massive" solution rather describes the gluon as a vector boson that features a finite Debye screening mass. In this work we examine the gauge dependence of these solutions by adopting stochastic quantization. What we find, in four dimensions and in a rainbow approximation, is that stochastic quantization supports both solutions in Landau gauge but the scaling solution abruptly disappears when the parameter controlling the drift force is separated from zero (soft gauge-fixing), recovering only the perturbative propagators; the massive solution seems to survive the extension outside Landau gauge. These results are consistent with the scaling solution being related to the existence of a Gribov horizon, with the massive one being more general. We also examine the effective action in Faddeev-Popov quantization that generates the rainbow and we find, for a bare vertex approximation, that the the massive-type solutions minimise the quantum effective action.

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