For a prototypical first-class system, dual-BRST and anti-dual-BRST symmetries are obtained from ordinary BRST and anti-BRST symmetries by canonical relabeling of ghost variables, so they are not independent symmetries.
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Forms of BRST symmetry on a Prototypical First-Class System
For a prototypical first-class system, dual-BRST and anti-dual-BRST symmetries are obtained from ordinary BRST and anti-BRST symmetries by canonical relabeling of ghost variables, so they are not independent symmetries.