Semidensities, Second-Class Constraints and Conversion in Anti-Poisson Geometry
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Physics |
| MU Faculty or unit | |
| Citation | |
| Web | http://arxiv.org/abs/0705.3440 |
| Doi | http://dx.doi.org/10.1063/1.2890672 |
| Field | Theoretical physics |
| Keywords | Batalin-Vilkovisky Field-Antifield Formalism; Odd Laplacian; Anti-Poisson Geometry; Semidensity; Second-Class Constraints; Conversion. |
| Description | 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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