Yang-Mills Integrals

TL;DR

This paper introduces new analytical methods for evaluating reduced Yang-Mills integrals, providing compact representations and explicit calculations for low-order cases, exemplified by real symmetric matrices of order 3.

Contribution

It presents a compact integral representation and an analytical evaluation method for low-order Yang-Mills integrals with different symmetry groups and dimensions.

Findings

Derived a compact integral representation for reduced Yang-Mills integrals.

Developed a method for analytical evaluation of low-order integrals.

Successfully evaluated a Yang-Mills integral over real symmetric matrices of order 3.

Abstract

Two results are presented for reduced Yang-Mills integrals with different symmetry groups and dimensions: the first is a compact integral representation in terms of the relevant variables of the integral, the second is a method to analytically evaluate the integrals in cases of low order. This is exhibited by evaluating a Yang-Mills integral over real symmetric matrices of order 3.