On odd Laplace operators. II

@article{Khudaverdian2002OnOL,
  title={On odd Laplace operators. II},
  author={Hovhannes M. Khudaverdian and Theodore Th. Voronov},
  journal={arXiv: Differential Geometry},
  year={2002}
}
We analyze geometry of the second order differential operators, having in mind applications to Batalin--Vilkovisky formalism in quantum field theory. As we show, an exhaustive picture can be obtained by considering pencils of differential operators acting on densities of all weights simultaneously. The algebra of densities, which we introduce here, has a natural invariant scalar product. Using it, we prove that there is a one-to-one correspondence between second-order operators in this algebra… 

Second order operators on the algebra of densities and a groupoid of connections

TLDR
This work considers the geometry of second order linear operators acting on the commutative algebra of densities on a (super)manifold and obtains operators that depend on equivalence classes of connections and a groupoid of connections such that the orbits of this groupoid are these equivalence Classes.

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