Integration measure and extended BRST-covariant quantization

We propose an extended BRST-invariant Lagrangian quantization scheme of general gauge theories based on explicit realization of the "modified triplectic algebra" that was announced in our previous investigation (hep-th/0104189). The algebra includes, besides the specific odd operators V-alpha appearing in the triplectic formalism, also the odd operators U-alpha introduced within modified triplectic quantization and the second-order odd operators Delta(alpha). While the operators V-alpha can be viewed as anti-Hamiltonian vector fields generated by a second-rank irreducible Sp(2) tensor, the operators U-alpha are the anti-Hamiltonian vector fields generated by a Sp(2) scalar. We show that some even supersymplectic structure, defined on the space of fields and antifields, provides the extended BRST path integral with a well-defined integration measure. All the known Lagrangian quantization schemes based on the extended BRST symmetry are obtained by specifying the (free) parameters of that method.