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首页> 外文期刊>Advances in high energy physics >A Global Approach with Cutoff Exponential Function, Mathematically Well Defined at the Outset, for Calculating the Casimir Energy: The Example of Scalar Field
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A Global Approach with Cutoff Exponential Function, Mathematically Well Defined at the Outset, for Calculating the Casimir Energy: The Example of Scalar Field

机译：一种具有截止指数函数的全局方法，该方法从一开始就在数学上得到了很好的定义，用于计算卡西米尔能量：标量场示例

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A global approach with cutoff exponential functions is used to obtain the Casimir energy of a masslessscalar field in the presence of a spherical shell. The proposed method, mathematically well defined at theoutset, makes use of two regulators, one of them to make the sum of the orders of Bessel functions finiteand the other to regularize the integral involving the zeros of Bessel function. This procedure ensures aconsistent mathematical handling in the calculations of the Casimir energy and allows a major comprehensionon the regularization process when nontrivial symmetries are under consideration. In particular, we determinethe Casimir energy of a scalar field, showing all kinds of divergences. We consider separately the contributions of the inner and outer regions of a spherical shell and show that the results obtained are in agreement withthose known in the literature, and this gives a confirmation for the consistence of the proposed approach. Thechoice of the scalar field was due to its simplicity in terms of physical quantity spin.
机译：具有截止指数函数的全局方法用于在球壳存在的情况下获得无质量标量场的卡西米尔能量。所提出的方法在一开始就在数学上得到了很好的定义，它利用两个调节器，其中一个使贝塞尔函数阶数之和为有限，另一个使与贝塞尔函数零有关的积分正规化。此过程可确保在卡西米尔能量的计算中进行一致的数学处理，并且在考虑非平凡对称性时可以对正则化过程有一个主要的了解。特别是，我们确定了标量场的卡西米尔能量，显示了各种散度。我们分别考虑了球形壳内部和外部区域的贡献，并表明获得的结果与文献中已知的结果一致，这为所提出方法的一致性提供了确认。选择标量场是由于其在物理量旋转方面的简单性。

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