Quantum dynamics of Lagrange multipliers

Abstract

When implementing a nonlinear constraint in quantum field theory by means of a Lagrange multiplier, lambda(x), it is often the case that quantum dynamics induce quadratic and even higher-order terms in. lambda(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) = det g mu nu (x) = -1).