Employing the $n_mu ^* $ prescription for axial-type gauges, and working in the unified-gauge formalism defined by nu03bc and the null vector Fu03bc, we develop a simple technique for evaluating higher-rank integrals from known lower-rank integrals. Based on partial differentiation and ...
Tkachov. New approach to evaluation of multiloop feynman integrals: The gegenbauer polynomial x-space technique. Nuclear Physics, B174:345-377, 1980.K.G. Chetyrkin, A.L. Kataev and F.V. Tkachov, New approach to evaluation of multiloop feynman integrals: the gegenbauer polynomial x space ...
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 in arbitrary space-time dimension. We introduce a ...
We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the example of multi-loop banana integrals. For example, we ...
The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently proposed technique for studying the recurrence relations as by-...
[12]However, a calculational technique that Feynman developed for gravity in 1962 — "ghosts" — later proved invaluable. In 1967, Fadeev and Popov quantized the particle behaviour of the spin 1 theories of Yang-Mills -Shaw -Pauli, that are now seen to describe the weak and strong ...
We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in ...
For a functional, the variables x and y become functions which we can expand out to a string of n quantities [say, s(x1); s(x2); : : : ; s(xn)] and the summations become integrals over dx1dx2 : : : dxn, so the analogous expression for a functional looks like X1 Z 1 F ...
A new integration technique for multi-loop Feynman integrals, called the matrix method, is presented. The new technique uses rotations in the combined space of the loop momenta to deal with overlapping loops. This procedure allows all momentum integrations to be carried out at the same time, ...
Furthermore, we show how to obtain Pfaffian systems of differential equations for the basis integrals using the same technique. All the steps are illustrated on the example of a two-loop non-planar triangle diagram with a massive loop. Keywords: Scattering Amplitudes, Differential and Algebraic ...