Reducing differential equations for multiloop master integrals
- 149 Downloads
We present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization parameter ϵ. We consider linear transformations of the functions column which are rational in the variable and in ϵ. Apart from some degenerate cases described below, the algorithm allows one to obtain the required transformation or to ascertain irreducibility to the form required. Degenerate cases are quite anticipated and likely to correspond to irreducible systems.
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- M.A. Barkatou and E. Pflügel, Computing super-irreducible forms of systems of linear differential equations via Moser-reduction: a new approach, in proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, Waterloo, Ontario, Canada, July 29 - August 1 2007, ACM, New York U.S.A. (2007), pp. 1-8.Google Scholar
- V. Zakharov, S. Manakov, S. Novikov and L. Pitaevsky, Soliton theory, in The inverse problem method, Nauka, Moscow Russia (1980).Google Scholar
- I. Gohberg, P. Lancaster and L. Rodman, Invariant subspaces of matrices with applications, Classics in Applied Mathematics (Book 51), SIAM (1986).Google Scholar