Related papers: A simple algorithm for automatic Feynman diagram g…
The symmetry factor of Feynman diagrams for real and complex scalar fields is presented. Being analysis of Wick expansion for Green functions, the mentioned factor is derived in a general form. The symmetry factor can be separated into two…
A numerical program is presented which facilitates a computation pertaining to the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such…
General formula for symmetry factors (S-factor) of Feynman diagrams containing fields with high spins is derived. We prove that symmetry factors of Feynman diagrams of well-known theories do not depend on spins of fields. In contributions…
Visual design is an essential application of state-of-the-art multi-modal AI systems. Improving these systems requires high-quality vision-language data at scale. Despite the abundance of internet image and text data, knowledge-rich and…
With the aid of simple examples we show how to make simple estimates of the sizes of higher-order Feynman graphs. Our methods enable appropriate values of renormalization and factorization scales to be made. They allow the diagnosis of the…
In a recent paper we introduced the chirality-flow formalism, a method for simple and transparent calculations of Feynman diagrams based on the left- and right-chiral $\mathrm{sl}(2,\mathbb{C})$ nature of spacetime. While our previous work…
Among 12672 Feynman diagrams contributing to the electron anomalous magnetic moment at the tenth order, 6354 are the diagrams having no lepton loops, i.e., those of quenched type. Because the renormalization structure of these diagrams is…
In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided that $\Delta^4=O(m)$, where $\Delta$ is the maximal degree and $m$ is the number of edges,the algorithm runs in expected…
A C-program DIANA (DIagram ANAlyser) for the automatic Feynman diagram evaluation is presented. It consists of two parts: the analyzer of diagrams and the interpreter of a special text manipulating language. This language is used to create…
We give a short introduction to Feynman diagrams, with many exercises. Text is targeted at students who had little or no prior exposure to quantum field theory. We present condensed description of single-particle Dirac equation, free…
We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams. Exact solutions…
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
This paper describes the Mathematica package FeynArts used for the generation and visualization of Feynman diagrams and amplitudes. The main features of version 3 are: generation of diagrams at three levels, user-definable model files,…
In this paper we present FeynRules, a new Mathematica package that facilitates the implementation of new particle physics models. After the user implements the basic model information (e.g. particle content, parameters and Lagrangian),…
We study those automatic sequences which are produced by an automaton whose underlying graph is the Cayley graph of a finite group. For $2$-automatic sequences, we find a characterization in terms of what we call homogeneity, and among…
We describe an efficient practical procedure for enumerating and regrouping vacuum Feynman graphs of a given order in perturbation theory. The method is based on a combination of Schwinger-Dyson equations and the two-particle-irreducible…
We introduce flat automata for automatic generation of tokenizers. Flat automata are a simple representation of standard finite automata. Using the flat representation, automata can be easily constructed, combined and printed. Due to the…
In the wake of the growing popularity of machine learning in particle physics, this work finds a new application of geometric deep learning on Feynman diagrams to make accurate and fast matrix element predictions with the potential to be…
A C-program DIANA (DIagram ANAlyser) for the automatic Feynman diagram evaluation is presented.
We introduce a novel compositional description of Feynman diagrams, with well-defined categorical semantics as morphisms in a dagger-compact category. Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning,…