Related papers: Noncommutative theories and general coordinate tra…
We study the space-time symmetries and transformation properties of the non-commutative U(1) gauge theory, by using Noether charges. We carry out our analysis by keeping an open view on the possible ways $\theta^{\mu \nu}$ could transform.…
Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved…
We introduce a new set of noncommutative space-time commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative space-time relations taken here to have position…
Considering that a position measurement can effectively involve a momentum-dependent shift and rescaling of the "true" space-time coordinates, we construct a set of effective space-time coordinates which are naturally non-commutative. They…
We investigate the effect of the noncommutative geometry on the classical orbits of particles in a central force potential. The relation is implemented through the modified commutation relations $[x_i, x_j]=i \theta_{ij} $. Comparison with…
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…
We study the cosmological aspects of a noncommutative, multidimensional universe where the matter source is assumed to be a scalar field which does not commute with the internal scale factor. We show that such noncommutativity results in…
For any adic transformation $T$ defined on the path space $X$ of an ordered Bratteli diagram, endowed with a Markov measure $\mu$, we construct an explicit dimension space (which corresponds to a matrix values random walk on $\mathbb{Z}$)…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…
We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its…
Noncommuting spatial coordinates are studied in the context of a charged particle moving in a strong non-uniform magnetic field. We derive a relation involving the commutators of the coordinates, which generalizes the one realized in a…
We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These…
Noncommutative coordinates are decomposed into a sum of geometrical ones and a universal quantum shift operator. With the help of this operator, the mapping of a commutative field theory into a noncommutative field theory (NCFT) is…
Turning on background fields in string theory sometimes has an alternative interpretation as a deformation of the target space geometry. A particularly well-known case is the NS-NS two form B, which gives rise to space-time…
These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…
The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the…
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…
The Einstein-Hilbert action in three dimensions and the transformation rules for the dreibein and spin connection can be naturally described in terms of gauge theory. In this spirit, we use covariant coordinates in noncommutative gauge…
We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation depends on a short-distance scale \ell_p, and thus breaks scale invariance, but preserves all space-time isometries. The…