Semidensities, Second-Class Constraints and Conversion in Anti-Poisson Geometry
Abstract
We consider Khudaverdian's geometric version of a Batalin-Vilkovisky (BV) operator \Delta_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 \Delta_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 \Delta_{E_D}, exactly follows from conversion of the antisymplectic second-class constraints into first-class constraints on an extended manifold.
Cite
@article{arxiv.0705.3440,
title = {Semidensities, Second-Class Constraints and Conversion in Anti-Poisson Geometry},
author = {K. Bering},
journal= {arXiv preprint arXiv:0705.3440},
year = {2008}
}