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

In quantum field theory, the in and out states can be related to the full Hamil-tonian by the ic 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 euro 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 Cesaro/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, indicat-ing advantages of these new methods over the existing methods in computation time and accuracy.