论文标题
紫外线发散和张量减少
UV Divergence and Tensor Reduction
论文作者
论文摘要
我们提出了一种有效的算法，以分解Feynman积分对局部差异和各种类型的亚差异的分解紫外线（UV）差异。通过一些合理的假设，Feynman积分的局部差异可以在维度正则化方案中唯一定义。通过在硬动量中的渐近扩展，局部和亚差异的计算减少为无质量真空积分局部差异的计算。在具有旋转$ \ le \ frac {1} {2} $的理论中，可以直接从积分的局部差异中提取beta函数和异常尺寸。 我们还提出了两种减少可用于计算局部差异的张量结构的方法。第一种方法是基于尺寸偏移的，对于具有循环编号$ l \ le3 $的积分非常强大。第二种方法是基于$ d _ {\ infty} $ dimension子空间的PV降低，并且更适合四个及以上的循环。
We present an efficient algorithm to decompose the ultraviolet (UV) divergences of Feynman integrals to local divergences and various types of sub-divergences. With some reasonable assumptions the local divergences of Feynman integrals can be uniquely defined in dimensional regularization scheme. By an asymptotic expansion in the hard momenta, the computation of local and sub-divergences is reduced to the computation of local divergences of massless vacuum integrals. In theories with spin $\le\frac{1}{2}$, the beta functions and anomalous dimensions can be extracted directly from the local divergence of integrals. We also propose two methods to reduce the tensor structures which can be used in the computation of local divergence. The first method is based on dimensional shift and is extremely powerful for integrals with loop number $L\le3$. The second method is based on a PV reduction in a $d_{\infty}$ dimension subspace, and it is more suited in four and more loops.
