Redundancy of the quantum level gauge condition

Abstract

The manifold Γ̂ defined by the equations of motion (EM) of the gauge and ghost fields w.r.t. the gauge-fixed action is regarded as a supercanonical line bundle over the manifold Γ defined by the EM of the gauge fields only w.r.t. the classical action. In this language the BRST operator Q is a local section of the bundle Γ̂. Using this we give a local expression for Q as being, on the other hand, the nilpotent exterior derivative on Γ with the ghost field Ψ as its generator. This fiber bundle setup allows us to prove that any ‘‘second level’’ gauge condition, i.e., a gauge condition on Γ̂ is equivalent to a gauge on the base manifold Γ and thus does not break the BRST symmetry of the quantized theory.