Related papers: Recursive Graphical Construction for Feynman Diagr…

We develop a systematic projector-based Feynman diagram framework that intrinsically encodes quantum geometry for nonlinear optical responses. By explicitly incorporating geometric quantities such as the quantum geometric tensor, quantum…

The diagrammatic coaction underpins the analytic structure of Feynman integrals, their cuts and the differential equations they admit. The coaction maps any diagram into a tensor product of its pinches and cuts. These correspond…

We present a study of atom-wall interactions in non-relativistic quantum electrodynamics by functional integral methods. The Feynman-Kac path integral representation is generalized to the case when the particle interacts with a radiation…

This article is devoted problems of electromagnetic interaction in curved spacetime. Such problems exist, in particular, when we investigate electromagnetic quantum processes near black holes. The generalization of reduction formalism…

We develop a Feynman rule for energy-level diagrams emphasizing their connections to the double-sided Feynman diagrams and physical processes in the Liouville space. Thereby we completely identify such diagrams and processes contributing to…

Due to the significant progress made in the implementation of quantum hardware, efficient methods and tools to design corresponding algorithms become increasingly important. Many of these tools rely on functional representations of certain…

We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…

We propose a new symbolic algorithm and a C++ program for generating and calculating supersymmetric Feynman diagrams for ${\cal N}=1$ supersymmetric electrodynamics regularized by higher derivatives in four dimensions. According to standard…

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of…

Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and…

The method proposed by Pratt to derive recursion relations for systems of degenerate fermions [Phys. Rev. Lett. 84, 4255 (2000), arXiv:nucl-th/9905055] relies on diagrammatic techniques. This efficient formalism assumes no explicit two-body…

In this note, we formulate the notions of the direct and inverse problems and contact points for the Feynman diagrams. For the electron-photon interaction case, the solutions of these direct and inverse problems are presented. The…

We present a formulation of quantum circuit diagrams based on the exponential map which provides a new way to calculate graphically with circuits. We present a sound list of rewrite rules for this formulation and demonstrate a variety of…

In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by…

Information about the number of Feynman graphs for a given physical process in a given field theory is especially useful for confirming the result of a Feynman graph generator used in an automatic system of perturbative calculations. A…

Diagrammatic techniques are well-known in the calculation of dispersion interactions between atoms or molecules. The multipolar coupling scheme combined with Feynman ordered diagrams significantly reduces the number of graphs compared to…

A method of Feynman diagrams summation, based on using Schwinger-Dyson equations and Ward identities, is verified by calculating some four-loop diagrams in N=1 supersymmetric electrodynamics, regularized by higher derivatives. In…

When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…

Vacuum energy and other spectral functions of Laplace-type differential operators have been studied approximately by classical-path constructions and more fundamentally by boundary integral equations. As the first step in a program of…

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…