When implementing a non-linear constraint in quantum field theory by means of a Lagrange multiplier, $ł(x)$, it is often the case that quantum dynamics induce quadratic and even higher order terms in $ł(x)$, which then does not enforce the constraint anymore. This is illustrated in the case of Unimodular Gravity, where the constraint is that the metric tensor has to be unimodular ($g(x)\equiv \det\,g_{\m\n}(x)=-1$).

12 pages, 2 figures. A change in the Acknowledgemwnts section