  We investigate the issue of coordinate redefinition invariance by carefully
performing nonlinear transformations in the discretized quantum mechanical path
integral. By resorting to hamiltonian path integral methods, we provide the
first complete derivation of the extra terms (beyond the usual jacobian term)
which arises in the action when a nonlinear transformation is made. We comment
on possible connections with the renormalization group, by showing that these
extra terms may emerge from a ``blocking" procedure. Finally, by performing
field redefinitions before and after dimensional reduction of a two dimensional
field theory, we derive an explicit form fo an extra term appearing in a field
theory.
