2023/11/22 by V. Mishnyakov, Mishnyakov, V., А. Морозов +3
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Physical sciences #Fractal and DNA sequence analysis #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2311.13524
openalex publication_date 2023/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present a review of the relations between various equations for maximal cut banana Feynman diagrams, i.e. amplitudes with propagators substituted with δ-functions. We consider both equal and generic masses. There are three types of equation to consider: those in coordinate space, their Fourier transform and Picard-Fuchs equations originating from the parametric representation. First, we review the properties of the corresponding differential operators themselves, mainly their factorization properties at the equal mass locus and their form at special values of the dimension. Then we study the relation between the Fourier transform of the coordinate space equations and the Picard-Fuchs equations and show that they are related by factorization as well. The equations in question are the counterparts of the Virasoro constraints in the much-better studied theory of eigenvalue matrix models and are the first step towards building a full-fledged theory of Feynman integrals, which will reveal their hidden integrable structure.