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Semidensities on Odd Symplectic Supermanifolds

- H. Khudaverdian
- Mathematics
- 27 December 2000

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.… Expand

Higher Poisson Brackets and Differential Forms

- H. Khudaverdian, T. Voronov
- Mathematics
- 25 August 2008

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… Expand

On Odd Laplace Operators

- H. Khudaverdian, T. Voronov
- Mathematics
- 18 May 2002

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… Expand

On odd Laplace operators. II

- H. Khudaverdian, T. Voronov
- Mathematics
- 22 December 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… Expand

OPERATOR PENCIL PASSING THROUGH A GIVEN OPERATOR

- A. Biggs, H. Khudaverdian
- Mathematics
- 28 January 2013

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… Expand

Geometry of differential operators, odd Laplacians, and homotopy algebras

- H. Khudaverdian, T. Voronov
- Mathematics
- 1 January 2004

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… Expand

Berezinians, Exterior Powers and Recurrent Sequences

- H. Khudaverdian, T. Voronov
- Mathematics
- 10 September 2003

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… Expand

Thick morphisms of supermanifolds, quantum mechanics, and spinor representation

- H. Khudaverdian, T. Voronov
- MathematicsJournal of Geometry and Physics
- 31 August 2019

Thick morphisms, higher Koszul brackets, and $L_{\infty}$-algebroids

- H. Khudaverdian, T. Voronov
- Mathematics
- 29 August 2018

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… Expand

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