AI 中文总结
本文研究彩虹时空的卡西米尔效应，推导修正后的卡西米尔能量与力表达式，分析不同彩虹函数下的变化规律，得到彩虹参数项的界限为10^-24量级。
AI 中文摘要
我们研究彩虹时空的卡西米尔效应，重点关注卡西米尔能量和力的领头阶修正。从彩虹时空中的标量场拉格朗日量出发，通过δ函数势引入平行板，得到对应的能量动量张量。将该能量动量张量表示为作用于格林函数的二次算子，求得其真空期望值。通过求解彩虹时空中标量场的欧拉-拉格朗日方程，得到格林函数解。将这些格林函数解代入能量动量张量的真空期望值，得到彩虹时空中修正后的卡西米尔能量和力的表达式。我们针对不同的彩虹函数选择，研究了形变后的卡西米尔力和能量随板间距的变化。结果表明，对于两种彩虹函数选择，卡西米尔能量和力的绝对值会减小或增大；而对于一种特定的彩虹函数选择，其结果与闵可夫斯基时空中的标准结果一致。将我们的结果与实验测得的卡西米尔力值对比，得到了依赖于彩虹参数项的界限为10^-24量级。
英文摘要
We investigate the Casimir effect in rainbow space-time, focusing on leading-order corrections to the Casimir energy and force. Starting with the scalar field Lagrangian in rainbow space-time, with parallel plates introduced through delta-function potentials, we find the corresponding energy-momentum tensor. We obtain the vacuum expectation value of this energy-momentum tensor by expressing it as a quadratic operator acting on the Green's function. By solving the Euler-Lagrange equation of a scalar field in rainbow space-time, we obtain the Green's function solutions. Employing these Green's function solutions in the vacuum expectation value of the energy-momentum tensor, we obtain the modified Casimir energy and Casimir force expressions in rainbow space-time. We study the variation of the deformed Casimir force and energy with the distance between the plates for different choices of rainbow functions. Our results show that for two choices of rainbow functions, the absolute value of the Casimir energy and force is decreasing or increasing, whereas for one specific choice of rainbow functions, it remains the same as the standard result in Minkowski space-time. Comparing our result with experimentally measured value of Casimir force, we obtain the bound on the rainbow parameter dependent terms to be of the order of 10^-24.
Comments13 pages, 2 figures
