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arXiv · 2202.06350

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

Duc Huy Tran·Yi Wang·Juanyi Yang·Yuhang Zhu
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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.

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Duc Huy Tran, Yi Wang, Juanyi Yang, Yuhang Zhu. 2022-02-13. Numerical prescriptions of early-time divergences of the in-in formalism. https://doi.org/10.1088/1475-7516%2F2022%2F07%2F014

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