where a similar formula exists for s α α ˙ ˙ . Here the last term is the gauge ambiguity, i.e. the freedom to add exact forms in the Z-space, and ϵ ϵ = ϵ ϵ ( Y , Z | x ) . One can gauge fix it to have ∂ ∂ α α ϵ ϵ = 0 . Then, one plugs the solution to the third equation, which of the same type, i.e. a differential equation of the first order in the Z-space. Its general solution is again given by the Poincare Lemma