A gauge invariant exact renormalisation group. (I)

A manifestly gauge invariant continuous renormalisation group flow equation is constructed for pule SU(N) gauge theory. The formulation makes sense without gauge fixing and manifestly gauge invariant calculations may thus he carried out. The flow equation is naturally expressed in terms of fluctuating Wilson loops, with the effective action appearing as an integral over a 'gas' of Wilson loops. AL 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.) (C) 2000 Elsevier Science B.V. All rights reserved.