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On one hand, by including the Lautrup-Nakanishi field $B^a$, we have an off-shell BRST formulation, i.e. we can prove the nilpotency of the BRST transformation without using the (Euler-Lagrange) equations of motion. On the other hand, for some applications, a simpler on-shell BRST formulation (where the Lautrup-Nakanishi field $B^a$ has been integrated ...

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