Defines higher Courant-Dorfman algebras and higher Poisson vertex algebras, relates them to dg symplectic manifolds of degree n, proves analogous properties to classical versions, and applies the framework to BFV current algebras.
Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications
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abstract
These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV-formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present a proof of the isomorphism between the graph complex and the Chevalley-Eilenberg complex of formal Hamiltonian vectors fields. We briefly discuss how these ideas can be extended to the infinite dimensional setting. These notes should be accessible to both physicists and mathematicians.
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Higher Courant-Dorfman algebras and associated higher Poisson vertex algebras
Defines higher Courant-Dorfman algebras and higher Poisson vertex algebras, relates them to dg symplectic manifolds of degree n, proves analogous properties to classical versions, and applies the framework to BFV current algebras.