Classical and quantum Tsallis distributions have been widely used in many branches of natural and social sciences. But, the quantum field theory of the Tsallis distributions is relatively a less explored arena. In this paper, we derive the expression for the thermal two-point functions in the Tsallis statistics with the help of the corresponding statistical mechanical formulations. We show that the quantum Tsallis distributions used in the literature appear in the thermal part of the propagator much in the same way the Boltzmann–Gibbs distributions appear in the conventional thermal field theory. As an application of our findings, we calculate the thermal mass in the ϕ4 scalar field theory within the realm of the Tsallis statistics.

中文翻译：

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来自热场理论的现象学 Tsallis 分布

经典和量子 Tsallis 分布已广泛用于自然科学和社会科学的许多分支。但是，Tsallis 分布的量子场论是一个相对较少探索的领域。在本文中，我们借助相应的统计力学公式推导出了 Tsallis 统计中热两点函数的表达式。我们表明，文献中使用的量子 Tsallis 分布出现在传播子的热部分中，与 Boltzmann-Gibbs 分布出现在传统热场理论中的方式非常相似。作为我们研究结果的应用，我们计算了φ4Tsallis 统计领域内的标量场论。