发表机构
Federal Rural University of Rio de Janeiro（里约热内卢联邦农村大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过维度约化研究非局域标量场在1+2维的有效模型，计算相互作用能并分析热力学，发现分数自由度并给出低温有效性界限。
AI 中文摘要
本文研究了一个非局域标量场理论向1+2维的维度约化。该非局域模型引入了一个轻质量参数作为标度，主要修正了理论的红外区域。我们将外部源约束在二维平面上，以获得有效的格林函数，并提出了1+2维中标量场的有效拉格朗日量。利用静态传播子，我们计算了平面空间中点状电荷之间的相互作用能。此外，我们评估了因果格林函数和费曼格林函数，并讨论了有效平面模型在树级上的幺正性。最后，我们采用松原形式体系来研究平面模型的热力学。精确的热自由能显示出运动学禁闭特有的分数自由度，并施加了严格低温有效性界限（$T \ll \Lambda$）以保持宏观热力学稳定性。
英文摘要
In this paper, we study the dimensional reduction of a nonlocal scalar field theory to 1+2 dimensions. This nonlocal model introduces a light mass parameter as a scale that primarily modifies the infrared regime of the theory. We constraint the external sources to a bidimensional plane to obtain the effective Green's function and propose an effective Lagrangian for the scalar field in 1+2 dimensions. Using the static propagator, we calculate the interaction energy between point-like charges in the planar space. Furthermore, we evaluate the causal and Feynman Green's functions, and discuss the unitarity of the effective planar model at tree level. Finally, we implement the Matsubara formalism to investigate the thermodynamics of the planar model. The exact thermal free energy shows the fractional degrees of freedom characteristic of kinematic confinement and imposes a strict low-temperature validity bound ($T \ll Λ$) to preserve the macroscopic thermodynamic stability.
Comments10 pages, 2 figures
