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

Source: [Semidensities, Second-Class Constraints and Conversion in Anti-Poisson Geometry](<https://www.sota2.com/research/paper/68fa233b2c2a3760193946ec>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:25.740Z

Authors: K. Bering

Published: 2007-05-23T18:09:57.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0705.3440>)

[PDF](<https://arxiv.org/pdf/0705.3440.pdf>)