When does a non-linear point transformation generate an extra O((h/2π)2) potential in the effective Lagrangian

It is known that when a non-linear point transformation is made in the path integral describing a quantum mechanical system, the effective Lagrangian picks up an extra potential which is not obtained by a naive change of integration variables. In field theory on the contrary it is known that such a term is not needed to keep dimensionally regularized complete Green functions invariant. The difference is explained as due to the different regularization procedures used in the two cases. This observation is then used to derive the expression for the extra potential for both the Lagrangian and the Hamiltonian version of the path integral. (Auth.)