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Batalin-Vilkovisky algebras are a new type of algebraic structure on graded vector spaces, which first arose in the work of Batalin and Vilkovisky on gauge fixing in quantum field theory. In this article, we show that there is a natural…

High Energy Physics - Theory · Physics 2008-11-26 Ezra Getzler

Inspired by the formulation of the Batalin-Vilkovisky method of quantization in terms of ``odd time'', we show that for a class of gauge theories which are first order in the derivatives, the kinetic term is bilinear in the fields, and the…

High Energy Physics - Theory · Physics 2009-10-22 O. F. Dayi

This paper is a continuation of "Quantization of Lie bialgebras I-IV". The goal of this paper is to define and study the notion of a quantum vertex operator algebra in the setting of the formal deformation theory and give interesting…

Quantum Algebra · Mathematics 2007-05-23 Pavel Etingof , David Kazhdan

Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed that the B-model of mirror symmetry should be described by a quantum field theory on a Calabi-Yau variety, which they called the Kodaira-Spenser theory (we call it the BCOV theory). This is the…

Quantum Algebra · Mathematics 2012-01-24 Kevin J. Costello , Si Li

This paper analyzes in details the Batalin-Vilkovisky quantization procedure for BF theories on n-dimensional manifolds and describes a suitable superformalism to deal with the master equation and the search of observables. In particular,…

Quantum Algebra · Mathematics 2009-10-31 Alberto S. Cattaneo , Carlo A. Rossi

A quantization of classical deformation theory, based on the Maurer-Cartan Equation $dS + \frac{1}{2}[S,S] = 0$ in dg-Lie algebras, a theory based on the Quantum Master Equation $dS + \hbar \Delta S + \frac{1}{2} \{S,S\} = 0$ in…

Quantum Algebra · Mathematics 2018-07-09 Alexander A. Voronov

The Wilson effective action for general Yang-Mills gauge theory is shown to satisfy the usual form of Batalin-Vilkovisky (BV) master equation, despite that a momentum cutoff apparently breaks the gauge invariance. In the case of Abelian…

High Energy Physics - Theory · Physics 2008-11-26 Takeshi Higashi , Etsuko Itou , Taichiro Kugo

The construction of the master T-operator recently suggested in Alexandrov et al. (arXiv:1112.3310) is applied to integrable vertex models and associated quantum spin chains with trigonometric R-matrices. The master T-operator is a…

Mathematical Physics · Physics 2015-06-05 A. Zabrodin

We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the…

High Energy Physics - Theory · Physics 2016-04-06 Damiano Anselmi

We apply the BV formalism to non-commutative field theories, introduce BRST symmetry, and gauge-fix the models. Interestingly, we find that treating the full gauge symmetry in non-commutative models can lead to reducible gauge algebras. As…

High Energy Physics - Theory · Physics 2014-11-20 Klaus Bering , Harald Grosse

The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in three dimensions induces…

High Energy Physics - Theory · Physics 2009-11-07 Noriaki Ikeda

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…

Quantum Algebra · Mathematics 2011-12-15 Jian Qiu , Maxim Zabzine

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…

Mathematical Physics · Physics 2025-12-16 Anibal M. Medina-Mardones , Bruno Vallette

We study four dimensional gauge theories in the context of an equivariant extension of the Batalin-Vilkovisky (BV) formalism. We discuss the embedding of BV Yang-Mills (YM) theory into a larger BV theory and their relation. Partial…

High Energy Physics - Theory · Physics 2023-08-21 Francesco Bonechi , Alberto S. Cattaneo , Maxim Zabzine

We present the construction of the classical Batalin-Vilkovisky action for topological Dirac sigma models. The latter are two-dimensional topological field theories that simultaneously generalise the completely gauged…

High Energy Physics - Theory · Physics 2023-02-01 Athanasios Chatzistavrakidis , Larisa Jonke , Thomas Strobl , Grgur Šimunić

We study deformations of the quantum conformal mechanics of De Alfaro-Fubini-Furlan with rational additional potential term generated by applying the generalized Darboux-Crum-Krein-Adler transformations to the quantum harmonic oscillator…

Mathematical Physics · Physics 2018-08-01 José F. Cariñena , Luis Inzunza , Mikhail S. Plyushchay

We construct a formal global quantization of the Poisson Sigma Model in the BV-BFV formalism using the perturbative quantization of AKSZ theories on manifolds with boundary and analyze the properties of the boundary BFV operator. Moreover,…

Mathematical Physics · Physics 2020-04-10 Alberto S. Cattaneo , Nima Moshayedi , Konstantin Wernli

We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows us to compute the cohomology of the…

Algebraic Geometry · Mathematics 2007-05-23 F. Malikov , V. Schechtman

A Batalin-Vilkovisky formalism is most general framework to construct consistent quantum field theories. Its mathematical structure is called {\it a Batalin-Vilkovisky structure}. First we explain rather mathematical setting of a…

Symplectic Geometry · Mathematics 2017-08-23 Noriaki Ikeda

Using technique of wheeled props we establish a correspondence between the homotopy theory of unimodular Lie 1-bialgebras and the famous Batalin-Vilkovisky formalism. Solutions of the so called quantum master equation satisfying certain…

Differential Geometry · Mathematics 2010-03-19 S. A. Merkulov