AI 中文总结
该研究计算了带恒定轴向挠率时空中理想导电平行板间的卡西米尔力，推导了修正后的光子色散关系，得到了卡西米尔压强的二阶修正，建立了量子真空现象与非黎曼几何的联系。
AI 中文摘要
我们计算了具有恒定轴向挠率的时空中，理想导电平行板之间的卡西米尔力。在有效场论框架内（其中挠率通过规范不变的陈-西蒙斯型相互作用与电磁 sector 耦合），我们推导了修正后的光子色散关系和模式谱。利用ζ函数正则化，我们得到了真空能量以及挠率参数二阶的卡西米尔压强。我们的计算得到的修正项标度为ΔP/P₀ = -5ξ²S_z²a²/(4π²) + O(S_z⁴)，对应于有吸引力的卡西米尔力的轻微减弱。我们注意到文献中一个已知的微妙之处：由于陈-西蒙斯相互作用是全导数，一些分析得出它对标准边界条件下的卡西米尔能量无贡献，意味着领头阶修正为高阶的O(S_z⁴)。对于实验可实现的板间距（a ~ 1 μm），由于自旋-挠率耦合实验对宏观挠率的严格限制，该效应仍远低于当前探测阈值（|ΔP/P₀| ≲ 10⁻³⁰）。尽管如此，该计算在量子真空现象与非黎曼几何之间建立了一致的、规范不变的桥梁。我们讨论了有限温度效应和几何不对称性作为提高灵敏度的潜在途径，同时将结果置于动力学挠率、凝聚态类比和量子信息协议的更广泛背景下。我们的结果与标准模型扩展的CPT奇光子 sector 一致，并提供了用时空挠率解释洛伦兹破缺系数的几何方法。
英文摘要
We compute the Casimir force between perfectly conducting parallel plates in a spacetime endowed with constant axial torsion. Working within an effective field theory framework where torsion couples to the electromagnetic sector via a gauge-invariant Chern--Simons-type interaction, we derive the modified photon dispersion relation and mode spectrum. Using zeta-function regularization, we obtain the vacuum energy and the resulting Casimir pressure to second order in the torsion parameter. Our calculation yields a correction scaling as $ΔP/P_0 = -\frac{5ξ^2 S_z^2 a^2}{4π^2} + \order(S_z^4)$, which corresponds to a slight weakening of the attractive Casimir force. We acknowledge a known subtlety in the literature: because the Chern-Simons interaction is a total derivative, some analyses conclude that it should not contribute to the Casimir energy for standard boundary conditions, implying the leading correction is of higher order, $\order(S_z^4)$. For experimentally accessible plate separations ($a \sim \qty{1}{\micro\meter}$), the effect remains well below current detection thresholds ($|ΔP/P_0| \lesssim 10^{-30}$) due to stringent bounds on macroscopic torsion from spin-torsion coupling experiments. Nevertheless, the calculation establishes a consistent, gauge-invariant bridge between quantum vacuum phenomena and non-Riemannian geometry. We discuss finite-temperature effects and geometric asymmetries as potential pathways for enhancing sensitivity, while placing the results in the broader context of dynamical torsion, condensed matter analogs, and quantum information protocols. Our results are consistent with the CPT-odd photon sector of the Standard-Model Extension and provide a geometric interpretation of Lorentz-violating coefficients in terms of spacetime torsion.
Comments10 pages
