Projective Connections and Schwarzian Derivatives for Supermanifolds, and Batalin-vilkovisky Operators
نویسنده
چکیده
We extend the notion of a Thomas projective connection (a projective equivalence class of linear connections) for supermanifolds. As a by-product, we arrive at a generalisation of the multidimensional Schwarzian derivative for the super case which was previously unknown. This is combined with our previous construction of a Laplacian on the algebra of densities for a projectively connected manifold and allows us to study BatalinVilkovisky type operators and the relation between projective connections and odd Poisson structures.
منابع مشابه
Batalin–vilkovisky Formalism and Integration Theory on Manifolds
The correspondence between the BV-formalism and integration theory on supermanifolds is established. An explicit formula for the density on a Lagrangian surface in a superspace provided with an odd symplectic structure and a volume form is proposed.
متن کاملar X iv : h ep - t h / 92 05 08 8 v 1 2 6 M ay 1 99 2 Geometry of Batalin - Vilkovisky quantization
A very general and powerful approach to quantization of gauge theories was proposed by Batalin and Vilkovisky [1],[2]. The present paper is devoted to the study of geometry of this quantization procedure. The main mathematical objects under consideration are P -manifolds and SP -manifolds (supermanifolds provided with an odd symplectic structure and, in the case of SP -manifolds, with a volume ...
متن کاملar X iv : h ep - t h / 92 10 11 5 v 2 2 3 O ct 1 99 2 Semiclassical approximation in Batalin - Vilkovisky formalism
The geometry of supermanifolds provided with a Q-structure (i.e. with an odd vector field Q satisfying {Q, Q} = 0), a P -structure (odd symplectic structure ) and an S-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclass...
متن کاملDivergence Operators and Odd Poisson Brackets
We study various generating operators of a given odd Poisson bracket on a supermanifold. They arise as the operators that map a function to the divergence of the associated hamiltonian derivation, where divergences of derivations can be defined either in terms of berezinian volumes or of graded connections. Examples include generators of the Schouten bracket of multivectors on a manifold (the s...
متن کاملDeformations of Batalin–vilkovisky Algebras
We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of the Batalin–Vilkovisky algebra. While such an operator of order 2 defines a Lie algebra structure on A, an operator of an order higher than 2 (Koszul–Akman definition) leads to the structure of a strongly homotopy Lie algebra (L∞–algebra) on A. This allows us to give a defin...
متن کامل