Poisson structures in BRST–antiBRST invariant Lagrangian formalism

We show that the specific operators Va appearing in the triplectic formalism — the most general Sp(2) symmetric Lagrangian BRST quantization scheme — can be viewed as the anti-Hamiltonian vector fields generated by a second-rank irreducible Sp(2) tensor. This allows for an explicit realization of the “triplectic algebra” being constructed from an arbitrary Poisson bracket on the space of the fields only, equipped by the flat Poisson connection. We show that the whole space of fields and antifields can be equipped by an even supersymplectic structure, when this Poisson bracket is nondegenerate. This observation opens the possibility to provide the BRST/antiBRST path integral by a well-defined integration measure, as well as to establish a direct link between Sp(2) symmetric Lagrangian and Hamiltonian BRST quantization schemes.