论文标题
形式主义的早期分歧的数值处方
Numerical prescriptions of early-time divergences of the in-in formalism
论文作者
论文摘要
在量子场理论中，进出状态可以与$iε$处方有关的全哈密顿人有关。灯芯旋转可以进一步将相关函数带到欧几里得时空，在该时期，积分可以更好地定义。该设置方便用于分析计算。但是，对于数值计算，很难实现无限的$ε$或数值函数的芯子旋转。我们提出了两种新的数值方法来解决此问题，即基于线性回归和基于CESàRo/Riesz求和的Beta调节器方法的积分基础方法。还引入了先前在电磁工程中使用的另一种分区驱除方法。我们使用现有方法使用内形式主义积分来对这些方法进行基准测试，这表明这些新方法比计算时间和准确性中现有方法的优势。
In quantum field theory, the in and out states can be related to the full Hamiltonian by the $iε$ prescription. A Wick rotation can further bring the correlation functions to Euclidean spacetime where the integrals are better defined. This setup is convenient for analytical calculations. However, for numerical calculations, an infinitesimal $ε$ or a Wick rotation of numerical functions are difficult to implement. We propose two new numerical methods to solve this problem, namely an Integral Basis method based on linear regression and a Beta Regulator method based on Cesàro/Riesz summation. Another class of partition-extrapolation methods previously used in electromagnetic engineering is also introduced. We benchmark these methods with existing methods using in-in formalism integrals, indicating advantages of these new methods over the existing methods in computation time and accuracy.
