Related papers: Variations on Homological Reduction

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…

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…

We apply the BFFT formalism to a prototypical second-class system, aiming to convert its constraints from second- to first-class. The proposed system admits a consistent initial set of second-class constraints and an open potential function…

We reconsider the problem of BRST quantization of a mechanics with infinitely reducible first class constraints. Following an earlier recipe [Phys. Lett. B 381, 105, (1996)], the original phase space is extended by purely auxiliary…

We consider mechanical systems on $T^*M$ with possibly irregular and reducible first class contraints linear in the momenta, which thus correspond to singular foliations on $M$. According to a recent result, the latter ones have a…

We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. The approach is based on constructing the effective…

The hamiltonian BRST-anti-BRST theory is developed in the general case of arbitrary reducible first class systems. This is done by extending the methods of homological perturbation theory, originally based on the use of a single resolution,…

Constrained hamiltonian structure of noncommutative gauge theory for the gauge group U(1) is discussed. Constraints are shown to be first class, although, they do not give an Abelian algebra in terms of Poisson brackets. The related…

We study algebras constructed by quantum Hamiltonian reduction associated with symplectic quotients of symplectic vector spaces, including deformed preprojective algebras, symplectic reflection algebras (rational Cherednik algebras), and…

An irreducible Hamiltonian BRST-anti-BRST treatment of reducible first-class systems based on homological arguments is proposed. The general formalism is exemplified on the Freedman-Townsend model.

For a compact Lie group $G$ we consider a lattice gauge model given by the $G$-Hamiltonian system which consists of the cotangent bundle of a power of $G$ with its canonical symplectic structure and standard moment map. We explicitly…

We use the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) in order to convert second-class into first-class constraints for some quantum mechanics supersymmetric theories. The main point to be considered is that the extended…

On every split supermanifold equipped with the Rothstein even super-Poisson bracket we construct a deformation quantization by means of a Fedosov-type procedure. In other words, the supercommutative algebra of all smooth sections of the…

We define and study invariants which can be uniformly constructed for any gauge system. By a gauge system we understand an (anti-)Poisson supermanifold provided with an odd Hamiltonian self-commuting vector field called a homological vector…

An irreducible Hamiltonian BRST approach to topologically coupled p- and (p+1)-forms is developed. The irreducible setting is enforced by means of constructing an irreducible Hamiltonian first-class model that is equivalent from the BRST…

We give a quantum field theoretic derivation of the formula obeyed by the Ray-Singer torsion on product manifolds. Such a derivation has proved elusive up to now. We use a BRST formalism which introduces the idea of an infinite dimensional…

In this work, a method for solving the constraints of general relativity is presented, where first all geometrical objects are written in terms of a set of orthonormal triads and a flat Weitzenbock connection, which depends on the triads…

We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…

We show that it is possible to formulate the most general first-class gauge algebra of the operator formalism by only using BRST-invariant constraints. In particular, we extend a previous construction for irreducible gauge algebras to the…

This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity…