A Study To Examine Single-Variable Feyman Diagrams Utilising Differential Reduction Of Hypergeometric Functions

Abstract

This article uses Feynman diagrams as a framework to study the application of differential reduction methods to generalised hypergeometric functions in a one-variable setting. When assessing Feynman integrals, it is common practice to use generalised hypergeometric functions. These functions are fundamental to quantum field theory since they are used to calculate scattering amplitudes and other physical variables. Cutting down on the number of variables used in integrals from multiples to one may help make computations and analyses more efficient. Our study sheds light on the fundamental procedures and mathematical transformations required to accomplish this reduction by carefully analysing the methods. The approaches increase the practical applicability of theoretical physics, and we demonstrate this by presenting specific examples of how these methods simplify the calculation of Feynman diagrams. Based on these findings, differential reduction has the potential to become an invaluable resource in several branches of computer mathematics and high-energy physics.