Related papers: BV Formality
Kontsevich's formality theorem states that the differential graded Lie algebra of multidifferential operators on a manifold M is L-infinity-quasi-isomorphic to its cohomology. The construction of the L-infinity map is given in terms of…
The Batalin-Vilkovisky (BV) formalism is a powerful generalization of the BRST approach of gauge theories and allows to treat more general field theories. We will see how, starting from the case of a finite dimensional configuration space,…
In the classical Batalin--Vilkovisky formalism, the BV operator $\Delta$ is a differential operator of order two with respect to the commutative product. In the differential graded setting, it is known that if the BV operator is…
Recent developments of Batalin-Vilkovisky (BV) formalism and related geometry are reviewed. Mathematical structures of BV formalism are summarized as a Q-manifold and a QP-manifold. Lie algebras, Lie algebroids and other higher algebroids…
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…
We prove that the differential graded Lie algebra of functionals associated to the Chern-Simons theory of a semisimple Lie algebra is homotopy abelian. For a general field theory, we show that the variational complex in the…
The recently introduced equivariant BV formalism is extended to the case of manifolds with boundary under appropriate conditions. AKSZ theories are presented as a practical example.
We define a notion of astrongly homotopy BV algebra and apply it to deformation theory problems. Formality conjectures for Hochschild and cyclic chains are formulated. We prove some partial results supporting these conjectures.
This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we…
The search for algebraic foundations of colour-kinematics duality and the double-copy construction has brought into focus a generalization of Batalin--Vilkovisky algebras, referred to here as coexact BV-algebras and as…
The present work contains a complete formulation of the Batalin-Vilkovisky (BV) formalism in the framework of locally covariant field theory. In the first part of the thesis the classical theory is investigated with a particular focus on…
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…
We show that the Kaehler structure can be naturally incorporated in the Batalin-Vilkovisky formalism. The phase space of the BV formalism becomes a fermionic Kaehler manifold. By introducing an isometry we explicitly construct the fermionic…
We study linear Batalin-Vilkovisky (BV) quantization, which is a derived and shifted version of the Weyl quantization of symplectic vector spaces. Using a variety of homotopical machinery, we implement this construction as a symmetric…
We show that the Hochschild-Kostant-Rosenberg map from the space of multivector fields on a graded manifold N (endowed with a Berezinian volume) to the cohomology of the algebra of multidifferential operators on N (as a subalgebra of the…
The geometric interpretation of the Batalin-Vilkovisky antibracket as the Schouten bracket of functional multivectors is examined in detail. The identification is achieved by the process of repeated contraction of even functional…
We extend the formality theorem of Maxim Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes on smooth and complex manifolds.
We extend the formality theorem of M. Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes.
We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is…
The BV formalism is a well-established method for analyzing symmetries and quantization of field theories. In this paper we use the BV formalism to derive partition functions of gauge invariant operators up to equations of motions and their…