Related papers: Diagrammatic Coaction of Two-Loop Feynman Integral…
We introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we consider the Baikov representation of maximal cuts…
Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent hypergeometric functions of two variables $F_4$. These are defined for…
Multi-loop Feynman integrals are key objects for the high-order correction computations in high energy phenomenology. These integrals with multiple scales, may have complicated symbol structures. We show that the dual conformal symmetry…
Three-point vertex diagram plays a key role in the whole renormalization program of several QFT (quantum field theory) models such as QED, QCD, the Standard Model of eletroweak interactions and so forth. The exact analytic result for the…
It is shown how the geometrical splitting of N-point Feynman diagrams can be used to simplify the parametric integrals and reduce the number of variables in the occurring functions. As an example, a calculation of the…
An analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. The graph complex is generated by orientation classes of…
In this work, we study the computation of reduction coefficients for multi loop Feynman integrals using generating functions constructed within the Baikov representation. Compared with traditional Feynman rules, the Baikov formalism offers…
A set of programs is presented for automatically generating and calculating Feynman diagrams. Diagrams are generated with FeynArts, then algebraically simplified using a combination of Mathematica and FORM implemented in the package…
In the Symmetries of Feynman Integrals (SFI) approach, a diagram's parameter space is foliated by orbits of a Lie group associated with the diagram. SFI is related to the important methods of Integrations By Parts and of Differential…
It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.
Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…
An efficient way to calculate one-loop counterterms within the Feynman diagrammatic approach and dimensional regularization is to expand the propagators in the integrands of the Feynman integrals around vanishing external momentum. In this…
Feynman integrals with generic propagator powers in one and two spacetime dimensions are investigated from various perspectives. In particular, we argue that the class of track integrals at any loop order is fixed by the recently found…
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then,…
N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop…
We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, {\it i.e.}, the…
By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in…
We initiate a systematic framework for the analysis of analytic properties of finite Feynman integrals that are multiple polylogarithms. Based on the Feynman parameter representation in complex projective space, we make a complete…
Recently, an interesting pattern was found in the differential equations satisfied by the Feynman integrals describing tree-level correlators of conformally coupled scalars in a power-law FRW cosmology [1,2]. It was proven that simple and…
The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…