A Note on Semidensities in Antisymplectic Geometry
arXiv:hep-th/0604117 · doi:10.1063/1.2352859
Abstract
We revisit Khudaverdian's geometric construction of an odd nilpotent operator Δ_E that sends semidensities to semidensities on an antisymplectic manifold. We find a local formula for the Δ_E operator in arbitrary coordinates and we discuss its connection to Batalin-Vilkovisky quantization.
11 pages, LaTeX. v2: Added eqs. (4.1), (6.3), (6.4) & (6.5). v3: Sec. 6 expanded and ref. added. v4: Included a proof of the main statement in the appendices. v5: Flipped the sign convention for ν^{(2)}. v6: Stylistic changes