发表机构
The Ohio State University; Center for Cosmology and AstroParticle Physics (CCAPP); Department of Physics（俄亥俄州立大学; 宇宙学与天体粒子物理中心; 物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文计算了高温高密度QED在N³LO下O(e⁶)阶的红外敏感压强贡献，通过HTL重求和等方法推导，发现弱耦合与零温度极限不可交换。
AI 中文摘要
我们确定了高温高密度无质量量子电动力学（QED）中与红外敏感的压强贡献，其阶数为电荷e的O(e⁶)，得到了在热主导区域与简并区域之间的交叉区域均有效的表达式。该贡献源于硬热圈（HTL）重求和的软光子，其被单圈幂次修正或双圈次领头阶光子自能修饰。在分离静态与非静态部分后，我们得到了静态部分的闭合形式，并利用双伽马函数对非静态松原求和进行解析计算，将剩余的有限系数简化为一维数值积分。有限温度HTL抵消项在展开前抵消了因子化发散；在严格零温度T下，该发散则与硬四圈贡献抵消。在化学势为零时，静态部分重现了已知的完整O(e⁵)压强。对量纲正则化、未减除的非静态部分取冷极限，重现了正确的冷混合结果。关键的是，在任意固定T>0时，非静态结果关于e²保持解析。QED中零温度O(e⁶ ln e)项仅出现在非均匀极限T/m_E→0中，其中m_E为电屏蔽质量，这表明弱耦合极限与零温度极限不可交换。
英文摘要
We determine the infrared-sensitive contribution to the pressure of hot and dense massless quantum electrodynamics (QED) at $O({e}^6)$ in the electric charge $e$, obtaining a representation valid across the crossover between the thermally dominated and degenerate regimes. This contribution arises from a hard-thermal-loop (HTL) resummed soft photon dressed by either the one-loop power correction or the two-loop next-to-leading-order photon self-energy. After separating the static and nonstatic sectors, we obtain the static contribution in closed form and perform the nonstatic Matsubara sum analytically in terms of the digamma function, reducing the remaining finite coefficient to a one-dimensional numerical integral. The finite-temperature HTL counterterm cancels the factorization divergence before expansion; at strictly zero temperature $T$, this divergence instead cancels against the hard four-loop contribution. At vanishing chemical potential, the static sector reproduces the complete known $O\left(e^5\right)$ pressure. Taking the cold limit of the dimensionally regulated, unsubtracted nonstatic contribution reproduces the correct cold mixed result. Crucially, at any fixed $T>0$, the nonstatic result remains analytic in $e^2$. The zero-temperature $O(e^6\ln e)$ term in QED arises only in the nonuniform limit ${T}/{m_{\rm{E}}}\to0$ where $m_{\rm{E}}$ is the electric screening mass, demonstrating that the weak-coupling and zero-temperature limits do not commute.
Comments19 pages, 2 figures
