论文标题
在2+1尺寸的混合边界条件下对Casimir能量的辐射校正
Radiative Correction to The Casimir Energy with Mixed Boundary Condition in 2+1 Dimensions
论文作者
论文摘要
在本研究中，计算了零和无质量标量场对Casimir能量的零和一阶辐射校正，这些尺寸和无混合的（Neumann-Dirichlet）边界条件在2+1个维度的两个平行线之间进行了自我相互交互的$ ϕ^4 $理论的2+1维度。这项研究的要点是使用特殊程序来重新归一化Lagrangian的裸参数。重新归一化程序中使用的反术语是系统地依赖于位置的，与量子场上施加的边界条件一致。为了在Casimir能量的计算过程中正规化和去除无限态，使用了作为正则化技术的盒子减法方案。在此方案中，通常会引入两种类似的配置，并从适当限制的这两个配置的真空能相互减去。该问题的最终答案是有限的，并且与预期的物理基础一致。我们还将本文的新结果与先前报道的零和一阶辐射校正的结果与标量场的Casimir能量在两个空间维度中的Casimir能量，并具有周期性，迪里奇和Neumann边界条件。最后，讨论了此比较的所有方面。
In the present study, the zero- and first-order radiative correction to the Casimir energy for the massive and massless scalar field confined with mixed (Neumann-Dirichlet) boundary condition between two parallel lines in 2+1 dimensions for the self-interacting $ϕ^4$ theory was computed. The main point in this study is the use of a special program to renormalize the bare parameters of the Lagrangian. The counterterm used in the renormalization program, which was obtained systematically position-dependent, is consistent with the boundary condition imposed on the quantum field. To regularize and remove infinities in the calculation process of the Casimir energy, the Box Subtraction Scheme as a regularization technique was used. In this scheme, two similar configurations are usually introduced, and the vacuum energies of these two configurations in proper limits are subtracted from each other. The final answer for the problem is finite and consistent with the expected physical basis. We also compared the new result of this paper to the previously reported results in the zero- and first-order radiative correction to the Casimir energy of scalar field in two spatial dimensions with Periodic, Dirichlet, and Neumann boundary conditions. Finally, all aspects of this comparison were discussed.
