Ordered Exponential and Its Features in Yang-Mills Effective Action

TL;DR

This paper explores the properties of ordered exponentials on Riemannian manifolds and examines their role in the Yang-Mills effective action, highlighting new relations and open questions about divergences.

Contribution

It introduces novel relations for ordered exponentials and analyzes their impact on the structure of divergences in Yang-Mills theory.

Findings

Identified non-trivial relations for ordered exponentials.

Analyzed the dependence of Yang-Mills effective action on background fields.

Formulated open questions about divergence structures.

Abstract

In this paper we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds. As an example of application, we study a dependence of the four-dimensional quantum Yang-Mills effective action on the background filed and gauge transformations. Also, we formulate some open questions about a structure of divergences.