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The powerful quantization formalism of Batalin and Vilkovisky streamlines thederivation of the complete set of (non-linear) identities arising from thelocal BRST symmetry of Yang-Mills theories. When applied in the BackgroundField Method type of gauges, it also gives rise to identities which relateGreen's functions involving background fields to Green's functions involvingquantum fields. All these identities lie at the core of the recent progress inunderstanding from the continuum formulation the IR dynamics emerging fromlattice simulations. In this talk, we will first review the Batalin-Vilkoviskyformalism and then apply it to the problem of extracting the effective chargefrom the available lattice data.

IR properties of Yang-Mills theories from the Batalin-Vilkovisky formalism