A gauge invariant exact renormalisation group. (I) Original Research Article

A manifestly gauge invariant continuous renormalisation group flow equation is constructed for pure SU(N) gauge theory. The formulation makes sense without gauge fixing and manifestly gauge invariant calculations may thus be carried out. The flow equation is naturally expressed in terms of fluctuating Wilson loops, with the effective action appearing as an integral over a `gasʹ of Wilson loops. At infinite N, the effective action collapses to a path integral over the trajectory of a single particle describing one Wilson loop. We show that further regularisation of these flow equations is needed. (This is introduced in part II.)