Landau background gauge fixing and the IR properties of Yang-Mills Green functions

We analyze 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 behavior controls the IR properties of the gluon and the ghost propagators.

Figure 1

Contribution to ${\mathcal{G}}_{\mu \nu }$ from its connected components.

Figure 2

Iterative diagrammatic expansion of ${\Gamma }_{A^{*}\Omega }$.