Related papers: An introduction to the Batalin-Vilkovisky formalis…
In the preceding paper arXiv:0802.3252 [quant-ph] we treated a model given by a master equation with generalized Lindblad form, and examined the algebraic structure related to some Lie algebras and constructed an approximate solution. In…
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…
The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its…
We review the Schwinger-Keldysh, or in-in, formalism for studying quantum dynamics of systems out-of-equilibrium. The main motivation is to rephrase well known facts in the subject in a mathematically elegant setting, by exhibiting a set of…
Finite BRST-BV transformations are studied systematically within the W-X formulation of the standard and the Sp(2)-extended field-antifield formalism. The finite BRST-BV transformations are introduced by formulating a new version of the Lie…
The BRST quantization of strings is revisited and the derivation of the path integral measure for scattering amplitudes is streamlined. Gauge invariances due to zero modes in the ghost sector are taken into account by using the…
The extended phase space method of Batalin, Fradkin and Vilkovisky is applied to formulate two dimensional gravity in a general class of gauges. A BRST formulation of the light-cone gauge is presented to reveal the relationship between the…
The quantum Hamiltonian reduction on the OSp(1,2) super Kac-Moody algebra is described in the BRST formalism. Using a free field representation of the KM currents, the super Kac-Moody algebra is shown to be reduced to a superconformal one…
The Schr\"odinger-type formalism of the Klein-Gordon quantum mechanics is adapted for the case of the $SL(2,\R)$ spacetime. The free particle case is solved, the results of a recent work are reproduced while all the other, topologically…
It is well known that BRST symmetry plays a fundamental role in constructing quantum gauge theories. Yet, at the classical level, it constitutes the modern language to study constrained systems. First, this letter reviews the Sp(2)…
This note gives an introduction to Lagrangian field theories in the presence of boundaries. After an overview of the classical aspects, the cohomological formalisms to resolve singularities in the bulk and in the boundary theories (the BV…
We give a formal proof of the equivalence of Hamiltonian and Lagrangian BRST quantization. This is done for a generic $Sp(2)$-symmetric theory using flat (Darboux) coordinates. A new quantum master equation is derived in a Hamiltonian…
Closed string field theory leads to a generalization of Lie algebra which arose naturally within mathematics in the study of deformations of algebraic structures. It also appeared in work on higher spin particles \cite{BBvD}. Representation…
We study the Batalin-Vilkovisky master equation for both open and closed string field theory with special attention to anomalies. Open string field theory is anomaly free once the minimal coupling to closed strings induced by loop…
We derive equivariant localization formulas of Atiyah--Bott and cohomological field theory types in the Batalin-Vilkovisky formalism and discuss their applications in Poisson geometry and quantum field theory.
We describe a formalism underlying the renormalization procedure and Batalin-Vilkoviski formalism. In the framework of this formalism, we give a mathematical definition of OPE-algebra and describe an additional natural structure which…
The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…
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,…
This is the first in a series of papers on an attempt to understand quantum field theory mathematically. In this paper we shall introduce and study BV QFT algebra and BV QFT as the proto-algebraic model of quantum field theory by exploiting…
The Batalin-Vilkovisky method (BV) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close…