Related papers: ANATAR: AN Automated Tool for higher-order Amplitu…
Co-operation of the Feynman DIagram ANAlyzer (DIANA) with the underlying operational system (UNIX) is presented. We discuss operators to run external commands and a recent development of parallel processing facilities and an extension in…
In this paper, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with complex internal masses. Our analytic results presented in this report are valid for both real and complex internal masses. The…
This paper presents Loops On Retrieval Augmented Generation (LoRAG), a new framework designed to enhance the quality of retrieval-augmented text generation through the incorporation of an iterative loop mechanism. The architecture…
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral and triangular prismatic cells. The algebra…
We present SubTropica, a Mathematica package that performs symbolic integration of multi-polylogarithmic integrals using recent advances in tropical geometry. It focuses on the class of linearly-reducible Euler integrals, such as Feynman…
We present FMFT - a package written in FORM that evaluates four-loop fully massive tadpole Feynman diagrams. It is a successor of the MATAD package that has been successfully used to calculate many renormalization group functions at…
A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t.\ the dimension parameter $\ep$ can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we…
New developments concerning the extension of the Feynman diagram analyzer DIANA are presented. We discuss new graphics facilities, different approaches to automation of momenta distribution and parallel processing facilities. Furthermore…
A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary…
On-shell amplitude methods allow to derive one-loop renormalization effects from just tree-level amplitudes, with no need of loop calculations. We derive a simple formula to obtain the anomalous dimensions of higher-dimensional operators…
We present an algorithm for the integrand-level reduction of multi-loop amplitudes of renormalizable field theories, based on computational algebraic geometry. This algorithm uses (1) the Gr\"obner basis method to determine the basis for…
Finite Feynman integrals have been advocated as the optimal components for constructing a basis of master integrals in multiloop calculations, due to their improved analytic and numerical properties. In this paper, we show how the Loop-Tree…
We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced…
AMFlow is a Mathematica package to numerically compute dimensionally regularized Feynman integrals via the recently proposed auxiliary mass flow method. In this framework, integrals are treated as functions of an auxiliary mass parameter…
We present Version 8 of the Feynman-diagram calculator FormCalc. New features include in particular significantly improved algebraic simplification as well as vectorization of the generated code. The Cuba Library, used in FormCalc, features…
In the context of high-energy particle physics, a reliable theory-experiment confrontation requires precise theoretical predictions. This translates into accessing higher-perturbative orders, and when we pursue this objective, we inevitably…
The Noise-Directed Adaptive Remapping (NDAR) method utilizes amplitude damping noise to enhance the performance of quantum optimization algorithms. NDAR alternates between exploration by sampling solutions from the quantum circuit and…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
Higher transcendental function occur frequently in the calculation of Feynman integrals in quantum field theory. Their expansion in a small parameter is a non-trivial task. We report on a computer program which allows the systematic…
This study aims to improve knowledge-based question-answering (QA) systems by overcoming the limitations of existing Retrieval-Augmented Generation (RAG) models and implementing an advanced RAG system based on Graph technology to develop…