Explicit derivation of the QED trace anomaly in symmetry-preserving loop regularization at one-loop level
Explicit derivation of the QED trace anomaly in symmetry-preserving loop regularization at one-loop level
复制标题
单环级别保对称环正则化中 QED 迹异常的显式推导
DOI：
10.1103/physrevd.84.025020
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发表时间：
2011-03
期刊：
影响因子：
--
通讯作者：
Yue-Liang Wu
中科院分区：
文献类型：
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作者：
Jian-Wei Cui;Yong-Liang Ma;Yue-Liang Wu
基于在四维时空中实现的圈正则化方法，在单圈水平上计算了QED迹线反常，尽管引入了两个质量标度，即紫外（UV）截止M（c）和红外（IR）截止μ（s），但该方法仍保持了规范对称性和庞加莱对称性.结果表明，将三点图与真空极化图联系起来的膨胀Ward恒等式，通过取相容极限M（c）-> 1和μ（s）= 0的量子修正，得到了迹反常的标准形式，恢复了原始积分。这清楚地表明，循环正则化方法确实是一个自洽的正则化计划，这是适用于计算不仅手征异常，但也为痕量异常，至少在一个循环的水平。还可以看出，张量型和标量型不可约圈积分（ILI）的一致性条件是至关重要的，以获得一致的结果。作为比较，我们也给出了通常的Pauli-Villars正则化和维数正则化的单圈计算。
The QED trace anomaly is calculated at one-loop level based on the loop regularization method which is realized in 4-dimensional space-time and preserves gauge symmetry and Poincare symmetry in spite of the introduction of two mass scales, namely, the ultraviolet (UV) cutoff M(c) and infrared (IR) cutoff mu(s). It is shown that the dilation Ward identity which relates the three-point diagrams with the vacuum polarization diagrams gets the standard form of trace anomaly through quantum corrections in taking the consistent limit M(c) -> 1 and mu(s) = 0 which recovers the original integrals. This explicitly demonstrates that the loop regularization method is indeed a self-consistent regularization scheme which is applicable to the calculations not only for the chiral anomaly but also for the trace anomaly, at least at one-loop level. It is also seen that the consistency conditions which relate the tensor-type and scalar-type irreducible loop integrals (ILIs) are crucial for obtaining a consistent result. As a comparison, we also present the one-loop calculations by using the usual Pauli-Villars regularization and the dimensional regularization.