Semidensities, Second-Class Constraints and Conversion in Anti-Poisson Geometry
arXiv:0705.3440 · doi:10.1063/1.2890672
Abstract
We consider Khudaverdian's geometric version of a Batalin-Vilkovisky (BV) operator Δ_E in the case of a degenerate anti-Poisson manifold. The characteristic feature of such an operator (aside from being a Grassmann-odd, nilpotent, second-order differential operator) is that it sends semidensities to semidensities. We find a local formula for the Δ_E operator in arbitrary coordinates. As an important application of this setup, we consider the Dirac antibracket on an antisymplectic manifold with antisymplectic second-class constraints. We show that the entire Dirac construction, including the corresponding Dirac BV operator Δ_{E_D}, exactly follows from conversion of the antisymplectic second-class constraints into first-class constraints on an extended manifold.
32 pages, LaTeX. v2: Minor changes. v3: Published version