Twisted Feynman Integrals: from generating functions to spin-resummed post-Minkowskian dynamics
Abstract
We propose to call a class of deformed Feynman integrals as twisted Feynman integrals, where the integrand has an additional exponential factor linear in loop momenta. Such integrals appear in various contexts: tensor reduction of Feynman integrals, Fourier transform of Feynman integrals, and spin-resummed dynamics in post-Minkowskian gravity. First, we construct a mathematical framework that manifests the geometric interpretation of twisted Feynman integrals. Next, we generalise the standard mathematical tools for studying Feynman integrals for application to their twisted cousins, and explore their mathematical properties. In particular, it is found that (i) Symanzik polynomials are no longer homogeneous and become graded, (ii) twisted Feynman integrals fall under the class of exponential periods, and (iii) the geometry of the function space cannot be inferred from the leading singularity computed through the (generalised) Baikov parametrisation of twisted Feynman integrals.
Cite
@article{arxiv.2512.21210,
title = {Twisted Feynman Integrals: from generating functions to spin-resummed post-Minkowskian dynamics},
author = {Joon-Hwi Kim and Jung-Wook Kim and Jungwon Lim},
journal= {arXiv preprint arXiv:2512.21210},
year = {2026}
}
Comments
v2) 36 pages, 10 figures. Extended discussions on Symanzik polynomials and Fourier-transform approach to twisted Feynman integrals. Minor improvements for clarity; v1) 36 pages, 10 figures