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

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

2007-05-23

arxiv.org/abs/0705.3440v3

J.Math.Phys.49:043516,2008

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, LaTeX. v2: Minor changes. v3: Published version

Scientific paper

10.1063/1.2890672

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.

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