标题： 早时间发散的数值公式 显示英文标题

标题： Numerical prescriptions of early-time divergences of the in-in formalism

摘要： 在量子场论中，入射态和出射态可以通过$i\epsilon$处理与全哈密顿量相关联。维克转动可以进一步将关联函数带到欧几里得时空，在那里积分定义得更好。这种设置便于解析计算。然而，对于数值计算，实现无穷小的$\epsilon$或数值函数的维克转动是困难的。我们提出两种新的数值方法来解决这个问题，即基于线性回归的积分基方法和基于切萨罗/里斯求和的贝塔调节器方法。还介绍了另一类以前在电磁工程中使用的分区外推方法。我们使用入-入形式的积分对此类方法进行基准测试，表明这些新方法在计算时间和精度方面优于现有方法。 显示英文摘要

摘要： In quantum field theory, the in and out states can be related to the full Hamiltonian by the $i\epsilon$ 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 $\epsilon$ 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 Ces\`aro/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.