 First, instead of working with the gauge group "G" one can use only the action of the gauge algebra formula_8 on the fields (functions on the phase space).Second, the variation of any "BRST exact form" "sBX" with respect to a local gauge transformation "d"λ is

which is itself an exact form.More importantly for the Hamiltonian perturbative formalism (which is carried out not on the fiber bundle but on a local section), adding a BRST exact term to a gauge invariant Lagrangian density preserves the relation "sBX" = 0.