REDUNDANCY OF THE QUANTUM LEVEL GAUGE CONDITION

The manifold ($) over cap Gamma defined by the equations of motion (EM ) of the gauge and ghost fields w.r.t. the gauge-fixed action is regar ded as a supercanonical line bundle over the manifold Gamma defined by the EM of the gauge fields only w.r.t. the classical action. In this language the BRST operater Q is a local section of the bundle ($) over cap Gamma. Using this we give a local expression for Q as being, on t he other hand, the nilpotent exterior derivative on Gamma with the gho st field Psi as its generator. This fiber bundle setup allows us to pr ove that any ''second level'' gauge condition, i.e., a gauge condition on ($) over cap Gamma is equivalent to a gauge on the base manifold G amma and thus does not break the BRST symmetry of the quantized theory .