Related papers: Noncommutative Conformal Field Theory in the Twist…
We consider a noncommutative field theory with space-time $\star$-commutators based on an angular noncommutativity, namely a solvable Lie algebra: the Euclidean in two dimension. The $\star$-product can be derived from a twist operator and…
In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics,…
A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of functions by the noncommutative Moyal product, noncommutative…
This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry…
In this pedagogical mini course the basics of the derivation of the noncommutative structures appearing in string theory are reviewed. First we discuss the well established appearance of the noncommutative Moyal-Weyl star-product in the…
We present a classical conformal field theory on an arbitrary two-dimensional spacetime background. The dynamical object is a space-filling string, and the evolution may be thought as occurring on the manifold of the conformal group. The…
We argue that Poincar\'e symmetry can be implemented in NCFT if we allow the parameter of noncommutitive deformation $\theta^{\mu\nu}$ to change as a two-tensor under the corresponding space-time symmetry. The implementation is consistent…
We review aspects of our formalism for differential geometry on noncommutative and nonassociative spaces which arise from cochain twist deformation quantization of manifolds. We work in the simplest setting of trivial vector bundles and…
We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. This way symmetry…
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum…
Besides its various applications in string and D-brane physics, the $\theta$-deformation of space (-time) coordinates (naively called the noncommutativity of coordinates), based on the $\star$-product, behaves as a more general framework…
In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincar\'e invariance. We present the latest development in the field, in particular the notion of…
We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is…
In this Diploma-thesis models of gauge field theory on noncommutative spaces are studied. On the canonically deformed plane we discuss the dependence of the established gauge theory on the choice of the star product. Furthermore, gauge…
We consider a Moyal plane and propose to make the noncommutativity parameter \Theta^{\mu\nu} bifermionic, i.e., composed of two fermionic (Grassmann odd) parameters. The Moyal product then contains a finite number of derivatives, which…
This article reviews the construction and some applications of twisted Poincare-covariant quantum fields on the Moyal plane. The Drinfeld twist, which plays a key mathematical role in this construction, is then applied to the case of…
T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude.…
Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of…
Candidates for renormalisable gauge theory models on Moyal spaces constructed recently have non trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which…
In this paper, we study the corrections to tree level scattering that arise due to noncommutative deformations of cubic scalar field theory through implementation of the Groenewald-Moyal(GM) product. The additional noncommutative refinement…