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Semidensities on Odd Symplectic Supermanifolds
We consider semidensities on a supermanifold E with an odd symplectic structure. We define a new Δ-operator action on semidensities as the proper framework for the Batalin-Vilkovisky (BV) formalism.…
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Higher Poisson Brackets and Differential Forms
We show how the relation between Poisson brackets and symplectic forms can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential…
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On Odd Laplace Operators
We consider odd Laplace operators acting on densities of various weights on an odd Poisson (= Schouten) manifold M. We prove that the case of densities of weight 1/2 (half-densities) is distinguished…
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On odd Laplace operators. II
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…
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OPERATOR PENCIL PASSING THROUGH A GIVEN OPERATOR
Let Δ be a linear differential operator acting on the space of densities of a given weight λ0 on a manifold M. One can consider a pencil of operators Π(Δ)={Δλ} passing through the operator Δ such…
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Geometry of differential operators, odd Laplacians, and homotopy algebras
Abstract We give a complete description of differential operators generating a given bracket. In particular we consider the case of Jacobi-type identities for odd operators and brackets. This is…
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On complexes related with calculus of variations
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Berezinians, Exterior Powers and Recurrent Sequences
We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that traces of exterior powers of A satisfy universal recurrence relations…
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Thick morphisms of supermanifolds, quantum mechanics, and spinor representation
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Thick morphisms, higher Koszul brackets, and $L_{\infty}$-algebroids
It is a classical fact in Poisson geometry that the cotangent bundle of a Poisson manifold has the structure of a Lie algebroid. Manifestations of this structure are the Lichnerowicz differential on…
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