A Note on Semidensities in Antisymplectic Geometry
K. Bering
TL;DR
This paper revisits the geometric construction of an odd nilpotent operator acting on semidensities in antisymplectic geometry, providing a local formula and discussing its relevance to Batalin-Vilkovisky quantization.
Contribution
It offers a local coordinate formula for the elta_E operator and explores its connection to Batalin-Vilkovisky quantization, enhancing understanding of antisymplectic geometry.
Findings
Derived a local formula for elta_E in arbitrary coordinates
Clarified the connection between elta_E and Batalin-Vilkovisky quantization
Revisited Khudaverdian's geometric construction in a new light
Abstract
We revisit Khudaverdian's geometric construction of an odd nilpotent operator \Delta_E that sends semidensities to semidensities on an antisymplectic manifold. We find a local formula for the \Delta_E operator in arbitrary coordinates and we discuss its connection to Batalin-Vilkovisky quantization.
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