Coordinate redefinition invariance and ``extra'' terms

We investigate the issue of coordinate redefinition invariance by carefully performing non-linear transformations in the discretized quantum mechanical path integral. By resorting to hamiltonian path integral methods, we provide the first complete derivation of the extra term (beyond the usual jacobian term) which arises in the action when a non-linear transformation is made. We comment on possible connections with the renormalization group, by showing that these extra terms may emerge from a "blocking" procedure.