论文标题
阳米尔斯田的分形结构
Fractal structure of Yang-Mills fields
论文作者
论文摘要
在过去的几十年中，物理系统中非扩展热力学的起源一直在激烈争论。最近的结果表明，非扩展统计数据与热晶体之间存在联系。在回顾了这一联系之后，我们分析了阳米尔斯理论的缩放特性如何允许在仪表领域中出现自相似结构。这种结构的存在实际上是分形的，允许对顶点进行反复的非扰动计算。有人认为，当使用统计方法时，获得了非扩展统计信息，并且根据字段理论参数推导了Tsallis熵索引$ Q $。结果在一环近似中应用于QCD，从而与实验获得的$ q $值达成了良好的一致性。
The origin of non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Recent results indicate a connection between non-extensive statistics and thermofractals. After reviewing this connection, we analyze how scaling properties of Yang-Mills theory allow the appearance of self-similar structures in gauge fields. The presence of such structures, which actually behave as fractals, allows for recurrent non-perturbative calculations of vertices. It is argued that when a statistical approach is used, the non-extensive statistics is obtained, and the Tsallis entropic index, $q$, is deduced in terms of the field theory parameters. The results are applied to QCD in the one-loop approximation, resulting in a good agreement with the value of $q$ obtained experimentally.
