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Ordered Exponential and Its Features in Yang-Mills Effective Action

A. V. Ivanov, N. V. Kharuk

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.

Ordered Exponential and Its Features in Yang-Mills Effective Action

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.
Paper Structure (6 sections, 4 theorems, 54 equations)

This paper contains 6 sections, 4 theorems, 54 equations.

Table of Contents

  1. Introduction
  2. Ordered exponentials
  3. Additional properties
  4. Application to the Yang--Mills theory
  5. Conclusion
  6. Acknowledgements.

Key Result

Lemma 1

Let $x,y\in U$, and $1$ denotes the unit function. Then, under the conditions described above, we have

Theorems & Definitions (8)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof