2016/11/30 by C. Meyer, Christoph Meyer · 2 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algorithm #Applied mathematics #Basis (linear algebra) #Basis function #Black Holes and Theoretical Physics #Canonical form #Canonical transformation #Computation #Differential equation #Feynman diagram #Geometry #Loop (graph theory) #Mathematical analysis #Mathematical physics #Mathematics #Numerical methods for differential equations #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum #Quantum mechanics #Reduction (mathematics) #Standard basis #Transformation (genetics) #hep-ph #hep-th
paper · pdf · doi:10.1007/jhep04(2017)006
ancillary files provided; published version
openalex created_date 2016/11/11 · openalex publication_date 2017/04/01 · arxiv created 2017/05/22 · arxiv updated 2017/05/23 · openalex updated_date 2026/08/05
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.