Related papers: Coaction for Feynman integrals and diagrams
The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the $\epsilon$-expansion. As an example, we present a detailed discussion of…
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…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…
Recent developments in quantum chemistry, perturbative quantum field theory, statistical physics or stochastic differential equations require the introduction of new families of Feynman-type diagrams. These new families arise in various…
We present an interesting study of Feynman integral reduction that does not employ integration-by-parts identities. Our approach proceeds by studying the equivalence relations of integral contours in the Feynman parameterization. We find…
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…
The purpose of this paper is to show that, under certain combinatorial conditions on the graph, parametric Feynman integrals can be realized as periods on the complement of the determinant hypersurface in an affine space depending on the…
We present a new method for the momentum expansion of Feynman integrals with arbitrary masses and any number of loops and external momenta. By using the parametric representation we derive a generating function for the coefficients of the…
We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop…
We describe how a dlog representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized…
Some problems related to the structure of higher terms of the epsilon-expansion of Feynman diagrams are discussed.
We here give polynomial realizations of various Hopf algebras or bialgebras on Feynman graphs, graphs, posets or quasi-posets, that it to say injections of these objects into polynomial algebras generated by an alphabet. The alphabet here…
In quantum electrodynamics, optical processes are theoretically described by double-sided Feynman diagrams. This formalism is powerful in the case of molecules but proves inappropriate to account for light-matter interactions within complex…
We study the renormalization group equations following from the Hopf algebra of graphs. Vertex functions are treated as vectors in dual to the Hopf algebra space. The RG equations on such vertex functions are equivalent to RG equations on…
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees…
Graphical functions are special position space Feynman integrals, which can be used to calculate Feynman periods and one- or two-scale processes at high loop orders. With graphical functions, renormalization constants have been calculated…
This paper is an introduction to the language of Feynman Diagrams. We use Reshetikhin-Turaev graphical calculus to define Feynman diagrams and prove that asymptotic expansions of Gaussian integrals can be written as a sum over a suitable…
It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…
An algorithm for obtaining the Taylor coefficients of an expansion of Feynman diagrams is proposed. It is based on recurrence relations which can be applied to the propagator as well as to the vertex diagrams. As an application, several…
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.