A novel renormalizable representation of the Yang-Mills theory

Abstract

For a generic gauge-invariant correlator <{\cal Q}[A_μ]>_{A}, we reformulate the standard D=4 Yang-Mills theory as a renormalizable system of two interacting fields a_μ and B_μ which faithfully represent high- and low-energy degrees of freedom of the single gauge field A_μ in the original formulation. It opens a possibility to synthesize an infrared-nonsingular weak-coupling series, employed to integrate over a_μ for a given background B_μ, with qualitatively different methods. These methods are to be applied to evaluate the resulting (after the a_μ-integration) representation of <{\cal Q}[A_μ]>_{A} in terms of gauge-invariant generically non-local low-energy observables, like Wilson loops. The latter observables are averaged over B_μ with respect to a gauge-invariant Wilsonean effective action S_{eff}[B]. To avoid a destructive dissipation between the high- and low-energy excitations, we implement a specific fine-tuning of the interaction between the pair of the fields: prior to the integration over B_μ, the expectation value _{a} vanishes, in the tree order of the loop-wise expansion, for an arbitrary configuration of B_μ.