A Manifestly Gauge Invariant and Universal Calculus for SU(N) Yang-Mills

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU(N) Yang-Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the beta function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these non-universal contributions is done in an entirely diagrammatic fashion.