Abstract
We construct an improved Becchi-Rouet-Stora-Tyutin (BRST) operator and present generalizations of the standard BRST quantization and the BRST approach to Lie-algebra cohomology. In particular, we show how Lie-algebra two-cocycles can be related to an Osp(1,1\ensuremath{\Vert}2) generalization of the conventional BRST--anti-BRST algebra. As an application we consider open bosonic strings, and explicitly construct the improved BRST operator and the pertinent Osp(1,1\ensuremath{\Vert}2) algebra. We conclude that the string is naturally defined in a (D=28+2)-dimensional Parisi-Sourlas superspace, with phase-space Osp(1,1\ensuremath{\Vert}2) invariance generalized into a spacetime Osp(27,1\ensuremath{\Vert}2) covariance. We construct the Osp(27,1\ensuremath{\Vert}2)-covariant physical string states and establish their equivalence with the conventional D=26 transverse states through a quantum generalization of the Parisi-Sourlas dimensional reduction. We show how the additional two bosonic dimensions emerge from the conventional BRST approach and observe that the ghost number of Osp(1,1\ensuremath{\Vert}2)-invariant physical states vanishes.
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