Odd Scalar Curvature in Field-Antifield Formalism
| dc.creator | Batalin, Igor A. | |
| dc.creator | Bering, Klaus | |
| dc.date | 2007-08-02 | |
| dc.date | 2008-01-24 | |
| dc.date.accessioned | 2026-07-07T11:18:22Z | |
| dc.date.available | 2026-07-07T11:18:22Z | |
| dc.description | We consider the possibility of adding a Grassmann-odd function νto the odd Laplacian. Requiring the total Δoperator to be nilpotent leads to a differential condition for ν, which is integrable. It turns out that the odd function νis not an independent geometric object, but is instead completely specified by the antisymplectic structure E and the density ρ. The main impact of introducing the νterm is that it makes compatibility relations between E and ρobsolete. We give a geometric interpretation of νas (minus 1/8 times) the odd scalar curvature of an arbitrary antisymplectic, torsion-free and ρ-compatible connection. We show that the total Δoperator is a ρ-dressed version of Khudaverdian's Δ_E operator, which takes semidensities to semidensities. We also show that the construction generalizes to the situation where ρis replaced by a non-flat line bundle connection F. This generalization is implemented by breaking the nilpotency of Δwith an arbitrary Grassmann-even second-order operator source. | |
| dc.description | 23 pages, LaTeX. v2: More material added. v3: Reference added. v4: Grant number added. v5: Minor changes. v6: Stylistic changes | |
| dc.identifier | https://arxiv.org/abs/0708.0400 | |
| dc.identifier | http://arxiv.org/abs/0708.0400 | |
| dc.identifier | J.Math.Phys.49:033515,2008 | |
| dc.identifier | doi:10.1063/1.2835485 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/193319 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Symplectic Geometry | |
| dc.title | Odd Scalar Curvature in Field-Antifield Formalism | |
| dc.type | text |