Odd Scalar Curvature in Field-Antifield Formalism

dc.creatorBatalin, Igor A.
dc.creatorBering, Klaus
dc.date2007-08-02
dc.date2008-01-24
dc.date.accessioned2026-07-07T11:18:22Z
dc.date.available2026-07-07T11:18:22Z
dc.descriptionWe 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.description23 pages, LaTeX. v2: More material added. v3: Reference added. v4: Grant number added. v5: Minor changes. v6: Stylistic changes
dc.identifierhttps://arxiv.org/abs/0708.0400
dc.identifierhttp://arxiv.org/abs/0708.0400
dc.identifierJ.Math.Phys.49:033515,2008
dc.identifierdoi:10.1063/1.2835485
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/193319
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.titleOdd Scalar Curvature in Field-Antifield Formalism
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