分形、非广延统计与QCD
Fractals, non-extensive statistics and QCD
摘要：
本文分析了杨-米尔斯场论的标度性质如何通过标度演化表现为截断n点函数的自相似性。这种结构的存在，实际上表现为分形，允许任何顶点的经常性非微扰计算。一些一般性质确实与微扰阶无关，这简化了非微扰计算。我们表明，足够高的扰动订单的统计方法可以使用，非广泛的统计得到的Tsallis指数，$q$，推导出的场论参数。将所得结果应用于单圈近似下的QCD，计算了$q$，结果与实验值吻合较好。我们讨论了这种方法如何允许理解一些有趣的实验结果，在高能碰撞，作为行为的多重性对碰撞能量，长尾分布和分形维数中观察到的不对称性分析。
英文摘要：
In this work we analyse how scaling properties of Yang-Mills field theory manifest as self-similarity of truncated n-point functions by scale evolution. The presence of such structures, which actually behaves as fractals, allow for recurrent non-perturbative calculation of any vertex. Some general properties are indeed independent of the perturbative order, what simplifies the non-perturbative calculations. We show that for sufficiently high perturbative orders a statistical approach can be used, the non extensive statistics is obtained, and the Tsallis index, $q$, is deduced in terms of the field theory parameters. The results are applied to QCD in the one-loop approximation, where $q$ can be calculated, resulting in a good agreement with the value obtained experimentally. We discuss how this approach allows to understand some intriguing experimental findings in high energy collisions, as the behavior of multiplicity against collision energy, long-tail distributions and the fractal dimension observed in intermittency analysis.
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