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

Abstract

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.

C osmoWerth, Pinol, Renaux-Petel 2024Class. Quantum Grav.0000View full textAdd to dashboardCite

“…Even numerically, the convergence of the integrals in the UV with the iϵ prescription has always been a long-standing problem, see e.g [34][35][36][37]5.…”