In this study, we consider the four-dimensional Maxwell electrodynamics extended with CPT-even Myers-Pospelov Lorentz-violating dimension-six operators to investigate the associated two-dimensional properties in the context of quantum vacuum fluctuation effects, namely, the Casimir effect. Upon projecting out the 4D theory down to a 2D theory we obtain analogs of these operators leading to a modified dispersion relation in a Lorentz invariance violation (LIV) scalar model equivalent to the electromagnetic theory. By making use of the modified dispersion relation, we derive exact analytic expressions for the Casimir energy and force induced by imposing Dirichlet boundary conditions on the scalar field. In the regime where the LIV parameter becomes very small, we recover known results for the Casimir energy and force plus correction terms due to the LIV.

中文翻译：

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二维洛伦兹破坏卡西米尔效应

在这项研究中，我们考虑用 CPT 甚至 Myers-Pospelov Lorentz 破坏六维算子扩展四维麦克斯韦电动力学，以研究量子真空涨落效应（即卡西米尔效应）背景下相关的二维特性。将 4D 理论投影为 2D 理论后，我们获得了这些算子的类似物，从而导致了相当于电磁理论的洛伦兹不变性破坏 (LIV) 标量模型中修改后的色散关系。通过利用修正的色散关系，我们推导了在标量场上施加狄利克雷边界条件引起的卡西米尔能量和力的精确解析表达式。在 LIV 参数变得非常小的情况下，我们恢复了卡西米尔能量和力的已知结果以及 LIV 引起的修正项。