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arXiv · 0705.3440

Semidensities, Second-Class Constraints and Conversion in Anti-Poisson Geometry

K. Bering
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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.

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K. Bering. 2008-04-25. Semidensities, Second-Class Constraints and Conversion in Anti-Poisson Geometry. https://doi.org/10.1063/1.2890672

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