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Related papers: Deformation of Batalin-Vilkovisky Structures

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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

This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…

Mathematical Physics · Physics 2022-08-30 Kadri İlker Berktav

We consider semidensities on a supermanifold E with an odd symplectic structure. We define a new $\Delta$-operator action on semidensities as the proper framework for Batalin-Vilkovisky formalism. We establish relations between…

Differential Geometry · Mathematics 2007-05-23 Hovhannes Khudaverdian

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…

Representation Theory · Mathematics 2007-05-23 Alice Fialowski , Michael Penkava

Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations…

Mathematical Physics · Physics 2011-04-22 Detlev Buchholz , Gandalf Lechner , Stephen J. Summers

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…

Quantum Algebra · Mathematics 2011-03-31 Imma Galvez-Carrillo , Andy Tonks , Bruno Vallette

The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.

Rings and Algebras · Mathematics 2016-10-17 Mohamed Elhamdadi , Abdenacer Makhlouf

Three dimensional topological field theories associated with the three dimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are presented. These three dimensional monopole equations are obtained by a dimensional reduction…

High Energy Physics - Theory · Physics 2008-02-03 Yűji Ohta

We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…

High Energy Physics - Theory · Physics 2015-06-26 S. N. Solodukhin

In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…

Quantum Physics · Physics 2010-02-14 Philip Goyal

A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by several different frequency functions. This class of systems comprises all known cases of Hamiltonian Ermakov systems and can always be reduced to…

Mathematical Physics · Physics 2009-11-07 F. Haas , J. Goedert

A constructive procedure to obtain superintegrable deformations of the classical Smorodinsky-Winternitz Hamiltonian by using quantum deformations of its underlying Poisson sl(2) coalgebra symmetry is introduced. Through this example, the…

Mathematical Physics · Physics 2019-07-16 Angel Ballesteros Francisco J. Herranz , Fabio Musso , Orlando Ragnisco

We show that the axiom of Felder and Kazhdan on the vanishing of the cohomology groups in negative degree associated to solutions of the classical master equation in the Batalin-Vilkovisky formalism is violated by the spinning particle in a…

Mathematical Physics · Physics 2018-01-16 Ezra Getzler

A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.

High Energy Physics - Theory · Physics 2007-05-23 Michael Duetsch , Klaus Fredenhagen

We introduce and study deformation $T_{{\bf b},\phi}$ of Minkowski norms in $\mathbb{R}^n$, determined by a set ${\bf b}=(\beta_1,\ldots,\beta_p)$ of linearly independent 1-forms and a smooth positive function $\phi$ of $p$ variables. In…

Differential Geometry · Mathematics 2020-11-05 Vladimir Rovenski , Pawel Walczak

The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of…

Quantum Physics · Physics 2026-04-21 Kazutaka Takahashi , Pratik Nandy , Adolfo del Campo

We study the existence of a Batalin-Vilkovisky differential on the complete cohomology ring of a Frobenius algebra.We construct a Batalin-Vilkovisky differential on the complete cohomology ring in the case of Frobenius algebras with…

Representation Theory · Mathematics 2021-05-07 Tomohiro Itagaki , Katsunori Sanada , Satoshi Usui

The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base.…

Rings and Algebras · Mathematics 2015-06-23 Abdenacer Makhlouf

Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…

Rings and Algebras · Mathematics 2015-09-24 Ural Bekbaev

We review and extend the Alexandrov-Kontsevich-Schwarz-Zaboronsky construction of solutions of the Batalin-Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a…

Quantum Algebra · Mathematics 2007-05-23 Alberto S. Cattaneo , Giovanni Felder