Related papers: Noncommutative Gauge Fields on Poisson Manifolds
We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into a $\star$-product via an abelian twist (e.g. the Groenewold-Moyal twist). The Seiberg-Witten map between…
We consider a reduced model of four-dimensional Yang-Mills theory with a mass term. This matrix model has two classical solutions, two-dimensional fuzzy sphere and two-dimensional fuzzy torus. These classical solutions are constructed by…
We investigate the geometric, algebraic and homologic structures related with Poisson structure on a smooth manifold. Introduce a noncommutative foundations of these structures for a Poisson algebra. Introduce and investigate noncommutative…
This talk is an introduction to ideas of non-commutative geometry and star products. We will discuss consequences for physics in two different settings: quantum field theories and astrophysics. In case of quantum field theory, we will…
The concept of a noncommutative field is formulated based on the interplay between twisted Poincar\'e symmetry and residual symmetry of the Lorentz group. Various general dynamical results supporting this construction, such as the…
We construct a perturbative solution to classical noncommutative gauge theory on ${\mathbb{R}}^{3}$ minus the origin using the Groenewald-Moyal star product. The result describes a noncommutative point charge. Applying it to the quantum…
We show how to do gauge theory on the octonions and other nonassociative algebras such as `fuzzy $R^4$' models proposed in string theory. We use the theory of quasialgebras obtained by cochain twist introduced previously. The gauge theory…
A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar…
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to…
We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…
Noncommutative geometry is based on an idea that an associative algebra can be regarded as "an algebra of functions on a noncommutative space". The major contribution to noncommutative geometry was made by A. Connes, who, in particular,…
We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restrictions imposed by the associativity…
In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external…
We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive…
In this work we propose new non-commutative gauge theories that describe the dynamics of branes localized along twisted conjugacy classes on group manifolds. Our proposal is based on a careful analysis of the exact microscopic solution and…
We investigate the perturbative dynamics of noncommutative topologically massive gauge theories with softly broken supersymmetry. The deformed dispersion relations induced by noncommutativity are derived and their implications on the…
We discuss several examples of non-toric quiver gauge theories dual to Sasaki-Einstein manifolds with U(1)^2 or U(1) isometry. We give a general method for constructing non-toric examples by adding relevant deformations to the toric case.…
A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang-Mills theory is constructed and used to examine some generic properties of noncommutative quantum…
Gauge theories are formulated on the noncommutative two-sphere. These theories have only finite number of degrees of freedom, nevertheless they exhibit both the gauge symmetry and the SU(2) "Poincar\'e" symmetry of the sphere. In…