Related papers: Multiloop Feynman Integrals in the Worldline Appro…
As part of the study of the two-body problem in Einstein's gravity, the fourth post-Newtonian order (4PN) of the two-body effective action is being computed presently by both effective field theory (EFT) methods and others. Diagrams with 3…
We discuss the following recent applications of the ``string-inspired'' worldline technique to calculations in quantum electrodynamics: i) Photon splitting in a constant magnetic field, ii) The two-loop Euler-Heisenberg Lagrangian, iii) A…
Considerable work has been done on the one-loop effective action in combined electromagnetic and gravitational fields, particularly as a tool for determining the properties of light propagation in curved space. After a short review of…
The main goal of this paper is a direct diagrammatic evaluation of the effective four-photon Lagrangian of the Euler-Heisenberg type for the quantum electrodynamics of massive charged vector bosons. This QED model is naturally embedded in…
In this talk, we discuss recent progress in the application of generalizations of polylogarithms in the symbolic computation of multi-loop integrals. We briefly review the Maple program MPL which supports a certain approach for the…
A numerical technique for calculating effective actions of electromagnetic backgrounds is proposed, which is based on the string-inspired worldline formalism. As examples, we consider scalar electrodynamics in three and four dimensions to…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…
In this talk I discuss properties of the two Symanzik polynomials which characterise the integrand of an arbitrary multi-loop integral in its Feynman parametric form. Based on the construction from spanning forests and Laplacian matrices,…
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
We present explicit expressions for multi-fold logarithmic integrals that are equivalent to sums over polygamma functions at integer argument. Such relations find application in perturbative quantum field theory, quantum chemistry, analytic…
Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and…
This research note deals with the evaluation of some generalized beta-type integral operators involving the multi-index Mittag-Leffler function $E_{\epsilon_{i}),(\omega_{i})}(z)$. Further, we derive a new family of beta-type integrals…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…
We propose a new set of Master Integrals which can be used as a basis for certain multiloop calculations in massless gauge field theories. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The…
The Heisenberg-Euler Lagrangian is not only a topic of fundamental interest, but also has a rich variety of diverse applications in astrophysics, nonlinear optics and elementary particle physics etc. We discuss the series representation of…
We review the main steps of the differential equation approach to the analytic evaluation of Feynman graphs, showing at the same time its application to the 3-loop sunrise graph in a particular kinematical configuration.
We consider Feynman integrals with algebraic leading singularities and total differentials in $\epsilon\,\mathrm{d}\ln$ form. We show for the first time that it is possible to evaluate integrals with singularities involving unrationalizable…
We discuss a relation between two-loop bosonic worldline Green functions which are obtained by Schmidt and Schubert in two different parametrizations of a two-loop worldline. These Green functions are transformed into each other by some…