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arXiv 2006.00299hep-th
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d+1维Lorentz破坏标量场Casimir能量的辐射修正

Radiative Correction to the Casimir Energy for Lorentz-violating Scalar Field in d+1 Dimensions

M. A. Valuyan

摘要:

每个重整化理论中的重整化程序都应该与施加在量子场上的边界条件的类型一致地运行。为了保持这种一致性,反项通常以位置相关的形式出现。本文利用这些反项计算了d维空间中两平行平板间Dirichlet边界条件约束下有质量和无质量Lorentz破坏标量场的Casimir能量的辐射修正。在计算过程中,为了消除真空能量中出现的无穷大,采用了盒减法,并辅以截断正则化技术和解析延拓技术。通常,在盒减法方案中,定义两个相似的配置,并在适当的限度内将它们的真空能量彼此相减。我们的最终结果关于所有的空间维度是收敛的,并与预期的物理基础相一致。我们进一步绘制了类时和类空洛伦兹破坏系统的Casimir能量密度,在奇数和偶数维的数量,最终得到的结果的多个方面进行了讨论。

英文摘要:

The renormalization program in every renormalized theory should be run consistently with the type of boundary condition imposed on quantum fields. To maintain this consistency, the counterterms usually appear in the position-dependent form. In the present study, using such counterterms, we calculated the radiative correction to the Casimir energy for massive and massless Lorentz-violating scalar field constrained with Dirichlet boundary condition between two parallel plates in d spatial dimensions. In the calculation procedure, to remove infinities appearing in the vacuum energies, the box subtraction scheme supplemented by the cutoff regularization technique and analytic continuation technique were employed. Normally, in the box subtraction scheme, two similar configurations are defined and their vacuum energies are subtracted from each other in the appropriate limits. Our final results regarding all spatial dimensions were convergent and consistent with the expected physical basis. We further plotted the Casimir energy density for the time-like and space-like Lorentz-violating systems in a number of odd and even dimensions; multiple aspects of the obtained results were ultimately discussed.

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