Automated solution of first order factorizable systems of differential equations in one variable

DOI10.1016/j.nuclphysb.2018.12.010zbMath1409.81080arXiv1810.12261OpenAlexW2898129858WikidataQ128752383 ScholiaQ128752383MaRDI QIDQ1731637

Xianqiang Yang

Publication date: 13 March 2019

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.12261

Mathematics Subject Classification ID

Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18) Polylogarithms and relations with (K)-theory (11G55) Systems of linear first-order PDEs (35F35)

Related Items (27)

Three-loop effective potential of general scalar theory via differential equations ⋮ The two-loop massless off-shell QCD operator matrix elements to finite terms ⋮ Extremal black hole scattering at \(\mathcal{O} (G^3)\): graviton dominance, eikonal exponentiation, and differential equations ⋮ The polarized three-loop anomalous dimensions from on-shell massive operator matrix elements ⋮ The heavy fermion contributions to the massive three loop form factors ⋮ Hypergeometric structures in Feynman integrals ⋮ Three loop QCD corrections to the heavy-light form factors in the color-planar limit ⋮ The first-order factorizable contributions to the three-loop massive operator matrix elements \(A_{Qg}^{(3)}\) and \(\Delta A_{Qg}^{(3)}\) ⋮ The massless three-loop Wilson coefficients for the deep-inelastic structure functions \(F_2\), \(F_L\), \(xF_3\) and \(g_1\) ⋮ Numerical evaluation of iterated integrals related to elliptic Feynman integrals ⋮ The inverse Mellin transform via analytic continuation ⋮ Numerical implementation of harmonic polylogarithms to weight w = 8 ⋮ Subleading logarithmic QED initial state corrections to \(e^+ e^- \to \gamma^\ast / Z^{0^\ast}\) to \(O(\alpha^6 L^5)\) ⋮ The unequal mass sunrise integral expressed through iterated integrals on \(\overline{\mathcal{M}}_{1,3}\) ⋮ Modular transformations of elliptic Feynman integrals ⋮ The polarized transition matrix element \(A_{gq}(N)\) of the variable flavor number scheme at \(O(\alpha_s^3)\) ⋮ Sunrise integrals with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms ⋮ Solving nonlinear systems of fractional-order partial differential equations using an optimization technique based on generalized polynomials ⋮ Cuts and isogenies ⋮ Large Scale Analytic Calculations in Quantum Field Theories ⋮ The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements ⋮ On epsilon factorized differential equations for elliptic Feynman integrals ⋮ A Feynman integral depending on two elliptic curves ⋮ Analytic Integration Methods in Quantum Field Theory: An Introduction ⋮ Hypergeometric Functions and Feynman Diagrams ⋮ The SAGEX review on scattering amplitudes Chapter 3: Mathematical structures in Feynman integrals ⋮ The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

Uses Software

• FORM
• HarmonicSums
• Reduze
• Axodraw
• OreSys

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