English
Related papers

Related papers: Fedosov Deformation Quantization as a BRST Theory

200 papers

A geometric derivation of $W_\infty$ Gravity based on Fedosov's deformation quantization of symplectic manifolds is presented. To lowest order in Planck's constant it agrees with Hull's geometric formulation of classical nonchiral…

High Energy Physics - Theory · Physics 2015-06-26 Carlos Castro

A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic…

Mathematical Physics · Physics 2016-09-07 S. P. Hrabak

The BRST-anti-BRST covariant extension is suggested for the split involution quantization scheme for the second class constrained theories. The constraint algebra generating equations involve on equal footing a pair of BRST charges for…

High Energy Physics - Theory · Physics 2009-10-31 I. Yu. Karataeva , S. L. Lyakhovich

We develop BRST symmetry for the first time for a particle on the surface of a torus knot by analyzing the constraints of the system. The theory contains $2^{nd}$ class constraints and has been extended by introducing Wess-Zumino term to…

General Physics · Physics 2018-05-09 Vipul Kumar Pandey , Bhabani Prasad Mandal

The ``classical BRST construction'' as developed by Batalin-Fradkin-Vilkovisky is a homological construction for the reduction of the Poisson algebra $P = C^\infty (W)$ of smooth functions on a Poisson manifold $W$ by the ideal $I$ of…

q-alg · Mathematics 2016-09-08 Jim Stasheff

We observe that a system of irreducible, fiber-linear, first class constraints on T*M is equivalent to the definition of a foliation Lie algebroid over M. The BFV formulation of the constrained system is given by the Hamiltonian lift of the…

Mathematical Physics · Physics 2019-02-20 Noriaki Ikeda , Thomas Strobl

This is an expository note on Fedosov's construction of deformation quantization. Given a symplectic manifold and a connection on it, we show how to calculate the star-product step by step. We draw simple diagrams to solve the recursive…

Symplectic Geometry · Mathematics 2016-09-07 Olga Kravchenko

We show that every star product on a symplectic manifold defines uniquely a 1-differentiable deformation of the Poisson bracket. Explicit formulas are given. As a corollary we can identify the characteristic class of any star product as a…

Quantum Algebra · Mathematics 2007-05-23 Philippe Bonneau

We study the deformation quantisation (Moyal quantisation) of general constrained Hamiltonian systems. It is shown how second class constraints can be turned into first class quantum constraints. This is illustrated by the O(N) non-linear…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Frank Antonsen

We propose a program for bridging the gap between the perturbative BV-BFV quantization of Chern-Simons theory and the non-perturbative Reshetikhin-Turaev (RT) invariants of 3-manifolds, passing through factorization homology of…

Mathematical Physics · Physics 2026-04-07 Nima Moshayedi

The Fedosov deformation quantization of the symplectic manifold is determined by a 1-form differential r. We identify a class of r for which the $\star$ product becomes the Moyal product by taking appropriate Darboux coordinates, but…

High Energy Physics - Theory · Physics 2009-11-07 Shogo Aoyama , Takahiro Masuda

Model of noncommutative gravity is constructed by means of Fedosov deformation quantization of endomorphism bundle. The fields describing noncommutativity -- symplectic form and symplectic connection -- are dynamical, and the resulting…

High Energy Physics - Theory · Physics 2017-03-14 Michal Dobrski

We deform the moment map picture on the space of symplectic connections on a symplectic manifold. To do that, we study a vector bundle of Fedosov star product algebras on the space of symplectic connections. We describe a natural formal…

Symplectic Geometry · Mathematics 2021-06-28 Laurent La Fuente-Gravy

The curvature tensor of a symplectic connection, as well as its covariant derivatives, satisfy certain identities that hold on any manifold of dimension less than or equal to a fixed n. In this paper, we prove certain results regarding…

Differential Geometry · Mathematics 2024-02-06 Adrián Gordillo-Merino , Raúl Martínez-Bohórquez , José Navarro-Garmendia

We expose the basics of the Fedosov quantization procedure, placed in the general framework of symplectic ringed spaces. This framework also includes some Poisson manifolds with non regular Poisson structures, presymplectic manifolds,…

Symplectic Geometry · Mathematics 2015-06-26 Izu Vaisman

A Lagrangian BRST quantization for generic gauge theories in general irreducible non-Abelian hypergauges is proposed on a basis of the multilevel Batalin--Tyutin formalism and a special BV--BFV dual description for a reducible gauge model…

High Energy Physics - Theory · Physics 2019-04-16 Alexander A. Reshetnyak

In this paper we give a construction of Fedosov quantization incorporating the odd variables and an analogous formula to Getzler's pseudodifferential calculus composition formula is obtained. A Fedosov type connection is constructed on the…

Differential Geometry · Mathematics 2012-11-09 Camilo Mesa

A (biased and incomplete) review of the status of the theory of symplectic connections on supermanifolds is presented. Also, some comments regarding Fedosov's technique of quantization are made.

Differential Geometry · Mathematics 2012-05-02 José A. Vallejo

Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic…

Quantum Algebra · Mathematics 2020-04-10 Ryan E. Grady , Qin Li , Si Li

To exhibit the possible origin of the inner complexity of the Berkovits's pure spinor approach, we consider the covariant BRST quantization of the D=11 massless superparticle (M0-brane) in its spinor moving frame or twistor-like Lorentz…

High Energy Physics - Theory · Physics 2008-11-26 Igor A. Bandos