Related papers: Lectures on configuration space methods for sunris…
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of…
We introduce an efficient configuration space technique which allows one to compute a class of Feynman diagrams which generalize the scalar sunset topology to any number of massive internal lines. General tensor vertex structures and…
We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams (also called Bessel moments) which we use to numerically check on the correctness of the second order…
We derive recurrence relations for the calculation of multiloop sunset-type diagrams with large powers of massive propagators. The technique is formulated in configuration space and exploits the explicit form of the massive propagator…
We describe differential forms representing Feynman amplitudes in configuration spaces of Feynman graphs, and regularization and evaluation techniques, for suitable chains of integration, that give rise to periods of mixed Tate motives.
Configuration spaces form a rich class of topological objects which are not usually presented to an undergraduate audience. Our aim is to present configuration spaces in a manner accessible to the advanced undergraduate. We begin with a…
We determine the numerical values of scalar multi-loop two-vertex Feynman diagrams, the generalized sunset diagrams, by integrating all but the longitudinal momenta analytically. For the longitudinal momenta we introduce one collective…
Using dispersive techniques, it is possible to avoid ultraviolet divergences in the calculation of Feynman diagrams, making subsequent regularization of divergent diagrams unnecessary. We give a simple introduction to the most important…
A number of irreducible master integrals for L-loop sunrise-type and bubble Feynman diagrams with generic values of masses and external momenta are explicitly evaluated via Mellin-Barnes representation.
This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a…
The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an…
In this talk we discuss how ideas from the theory of mixed Hodge structures can be used to find differential equations for Feynman integrals. In particular we discuss the two-loop sunrise graph in two dimensions and show that these methods…
In theories like SM or MSSM with a complex gauge group structure the complete set of Feynman diagrams contributed to a particular physics process can be splited to exact gauge invariant subsets. Arguments and examples given in the review…
We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…
Recently, there has been an increased interest in the application of machine learning (ML) techniques to a variety of problems in condensed matter physics. In this regard, of particular significance is the characterization of simple and…
A new approach is introduced to study QCD amplitudes at high energy and comparatively small momentum transfer. Novel cut diagrams, representing resummation of Feynman diagrams, are used to simplify calculation and to avoid delicate…
Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…
We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational…
These are expanded lecture notes from lectures given at the Workshop on higher structures at MATRIX Melbourne. These notes give an introduction to Feynman categories and their applications. Feynman categories give a universal categorical…
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.