On the Landau Background Gauge Fixing and the IR Properties of YM Green Functions

TL;DR

This paper explores the algebraic structure of the background field method in Landau gauge Yang--Mills theory, revealing a unique Green function that governs the infrared behavior of gluon and ghost propagators, offering new insights into IR properties.

Contribution

It introduces a novel approach to analyze the IR behavior of Green functions in Landau gauge Yang--Mills theory, simplifying the algebraic structure and identifying a key Green function.

Findings

Identifies a unique Green function controlling IR behavior.

Shows structural simplifications in the background field method.

Provides a new framework for studying IR properties of YM Green functions.

Abstract

We analyse the complete algebraic structure of the background field method for Yang--Mills theory in the Landau gauge and show several structural simplifications within this approach. In particular we present a new way to study the IR behavior of Green functions in the Landau gauge and show that there exists a unique Green function whose IR behaviour controls the IR properties of the gluon and the ghost propagators.