Related papers: Direct Solution of Integration-by-Parts Systems
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…
Integration-by-parts (IBP) reduction is one of the essential steps in evaluating Feynman integrals. A modern approach to IBP reduction uses modular arithmetic evaluations with parameters set to numerical values at sample points, followed by…
An algorithm for the reduction of massive Feynman integrals with any number of loops and external momenta to a minimal set of basic integrals is proposed. The method is based on the new algorithm for evaluating tensor integrals,…
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,…
We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be…
Both nonzero temperature and chemical potentials break the Lorentz symmetry present in vacuum quantum field theory by singling out the rest frame of the heat bath. This leads to complications in the application of thermal perturbation…
A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
The defining equations for Killing vector fields and conformal Killing vector fields are overdetermined systems of PDE. This makes it difficult to solve the systems numerically. We propose an approach which reduces the computation to the…
The method of Symmetries of Feynman Integrals defines for any Feynman diagram a set of partial differential equations. On some locus in parameter space the equations imply that the diagram can be reduced to a linear combination of simpler…
We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…
We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of…
One of the most severe bottlenecks to reach high-precision predictions in QFT is the calculation of multiloop multileg Feynman integrals. Several new strategies have been proposed in the last years, allowing impressive results with deep…
We address the problem of unambiguous reconstruction of rational functions of many variables. This is particularly relevant for recovery of exact expansion coefficients in integration-by-parts identites (IBPs) based on modular arithmetic.…
In this paper, we develop an iterative sector-level reduction strategy for Feynman integrals, which bases on module intersection in the Baikov representation and auxiliary vector for tensor structure. Using this strategy we have studied the…
We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field…
We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted…
Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As…