Related papers: Lie algebraic Noncommutative Gravity
In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
It is shown that non-commutative spaces, which are quotients of associative algebras by ideals generated by non-linear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of…
Noncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal $\star$-product on…
The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance…
We review the first order theory of gravity (vierbein formulation) on noncommutative spacetime studied in [1, 2]. The first order formalism allows to couple the theory to fermions. This NC action is then reinterpreted (using the…
We review the connection between noncommutative field theories and gravity. When the noncommutativity is induced by the Moyal product we can use the Seiberg-Witten map in order to deal with ordinary fields. We then show that the effect of…
We consider the Hamiltonian BRST quantization of a noncommutative non abelian gauge theory. The Seiberg-Witten map of all phase-space variables, including multipliers, ghosts and their momenta, is given in first order in the noncommutative…
In this paper, we describe a method for obtaining the nonabelian Seiberg-Witten map for any gauge group and to any order in theta. The equations defining the Seiberg-Witten map are expressed using a coboundary operator, so that they can be…
The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an SL(2,C) formulation of gravity on such a…
We deform two-dimensional topological gravity by making use of its gauge theory formulation. The obtained noncommutative gravity model is shown to be invariant under a class of transformations that reduce to standard diffeomorphisms once…
In order to overcome ambiguity problem on identification of mathematical objects in noncommutative theory with physical observables, quantum mechanical system coupled to the NC U(1) gauge field in the noncommutative space is reformulated by…
We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein-Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric…
We show that noncommutative gauge theories with arbitrary compact gauge group defined by means of the Seiberg-Witten map have the same one-loop anomalies as their commutative counterparts. This is done in two steps. By explicitly…
We exploit the Seiberg-Witten maps for fields and currents in a U(1) gauge theory relating the noncommutative and commutative (usual) descriptions to obtain the O(\theta) structure of the commutator anomalies in noncommutative…
We show that noncommuting electric fields occur naturally in $\theta$-expanded noncommutative gauge theories. Using this noncommutativity, which is field dependent, and a hamiltonian generalisation of the Seiberg-Witten Map, the algebraic…
Massive vector fields can be described in a gauge invariant way with the introduction of compensating fields. In the unitary gauge one recovers the original formulation. Although this gauging mechanism can be extended to noncommutative…
An enveloping algebra valued gauge field is constructed, its components are functions of the Lie algebra valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of…
We show that the Seiberg-Witten map for a noncommutative gauge theory involves a noncommutative 1-cocycle. The cocycle condition enforces a consistency requirement, which has been previously derived.
We outline the the geometry of locally anisotropic (la) superspaces and la-supergravity. The approach is backgrounded on the method of anholonomic superframes with associated nonlinear connection structure. Following the formalism of…