2021/06/30 by James P. Edwards, Universidad Michoacana de San Nicol&, C. Moctezuma Mata +7
Mathematics · Physics and Astronomy · #Algebra over a field #Amplitude #Applied mathematics #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Feynman diagram #Feynman integral #Formalism (music) #Integration by parts #Mathematical analysis #Mathematical physics #Mathematics #Network topology #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #String theory #Theoretical physics #hep-ph #hep-th #msc:11B68 #msc:33C65 #msc:81Q30
paper · pdf · doi:10.3842/sigma.2021.065
published as SIGMA 17 (2021), 065, 19 pages · Based on the talk given by C. Schubert at "Algebraic Structures in Perturbative Quantum Field Theory", a conference in honor of Dirk Kreimer's 60th birthday
arxiv created 2021/07/03 · openalex publication_date 2021/07/03 · arxiv updated 2021/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it allows one to write down integral representations combining the contributions of large classes of Feynman diagrams of different topologies. However, calculating these integrals analytically without splitting them into sectors corresponding to individual diagrams poses a formidable mathematical challenge. We summarize the history and state of the art of this problem, including some natural connections to the theory of Bernoulli numbers and polynomials and multiple zeta values.