一种计算散射积分的新方法
A novel way of calculating scattering integrals
摘要：
这项技术被他们的发现者称为NDIM -负维积分法，依赖于三个方面的基础：高斯积分，级数展开和解析延拓。该技术已成功地应用于计算一般维正则化空间中的协变和非协变Feynman积分，即，D维时空，包括负域值。由于维数是一般的，我们可以专门用于一维积分。在这项工作中，我们展示了如何这种技术可以应用到解决某些不当积分，并给出了一个例子，出现在量子力学散射过程中的一个特殊的不当积分。传统上，广义积分是通过极限方法或已知的，由柯西主值通过留数概念技术赋予某些值。在这里，我们使用NDIM方法进行计算，并显示它对不当积分的效果很好。我们认为这种新颖的方法更简单，不需要像传统方法那样处理极点、残差或困难的闭合轮廓。
英文摘要：
The technique coined as NDIM - Negative Dimensional Integration Method by their discoverers, relies on a three-pronged basis: Gaussian integration, series expansion and analytic continuation. The technique has been successfully applied to the calculation of covariant and non covariant Feynman integrals in a generic dimensional regularization space, i.e., D-dimensional space-time for D including the negative domain values. Since the dimensionality is general, we can use specifically for one-dimensional integrals. In this work we show how this technique can be applied to tackle certain improper integrals and give an example of a particular improper integral that appears in quantum mechanical scattering process. Traditionally, improper integrals are ascribed certain values through the limiting approach or as is known, by the Cauchy principal value via residues concept technique. Here we use the NDIM approach to do the calculations and show it works fine for the improper integrals. This novel approach we believe is more straightforward and does not require to handle poles, residues, or difficult closed contours as in the traditional approach.
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