发表机构
Universidade Estadual do Ceará（塞阿拉州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析分形规范场在平行边界间的零温和有限温卡西米尔效应，发现快支速度为光速时压强为电磁值的2.21倍，高温极限比值为2.5，揭示多支结构的谱特征。
AI 中文摘要
我们研究了自由无迹标量荷分形规范场在两个平行反射边界之间的零温和有限温卡西米尔相互作用。变分分析确定了一个一致的边值问题，该问题约束了秩二场的所有五个物理极化。谱分为三个较快和两个较慢的传播模式。在零温下，真空相互作用按传播速度对模式加权；当快支速度设为光速时，所得卡西米尔压强约为理想电磁值的2.21倍。在有限温下，两支获得不同的热权重并产生分裂的交叉。归一化自由能和压强遵循不同的交叉轮廓，但相对于理想电磁学，趋近于相同的经典高温比值2.5，因为Matsubara零模独立于传播速度计数五个受限极化。我们推导了精确的热相互作用、其低温和高温极限，以及交叉尺度对有效规范场速度的依赖。从速度加权的量子涨落到经典模式计数的转变，提供了高阶规范场多支结构的直接谱特征。
英文摘要
We investigate the zero- and finite-temperature Casimir interaction of the free trace-full scalar-charge fracton gauge field between two parallel reflecting boundaries. A variational analysis determines a consistent boundary-value problem that confines all five physical polarizations of the rank-two field. The spectrum separates into three faster and two slower propagating modes. At zero temperature, the vacuum interaction weights the modes by their propagation speeds; when the fast-branch speed is set equal to the speed of light, the resulting Casimir pressure is approximately 2.21 times the ideal electromagnetic value. At finite temperature, the two branches acquire different thermal weights and generate a split crossover. The normalized free energy and pressure follow distinct crossover profiles but approach the same classical high-temperature ratio of 2.5 relative to ideal electromagnetism, because the Matsubara zero mode counts the five confined polarizations independently of their propagation speeds. We derive the exact thermal interaction, its low- and high-temperature limits, and the dependence of the crossover scale on the effective gauge-field velocity. The transition from velocity-weighted quantum fluctuations to classical mode counting provides a direct spectral signature of the multi-branch structure of the higher-rank gauge field.
Comments25 pages, 1 figure
