Related papers: Noncommutative fields in curved space
In this paper we extend the analysis of magnetic monopoles in quantum mechanics in three dimensional rotationally invariant noncommutative space $\textbf{R}^3_\lambda$. We construct the model step-by-step and observe that physical objects…
The aim of this thesis is to study the isopectral deformations from the point of view of Alain Connes' noncommutative geometry. This class of quantum spaces constituts a curved space generalisation of Moyal planes and noncommutative tori.…
Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing Mimetic Dark Matter models.…
We clarify the relation between noncommutative spacetimes and multifractional geometries, two quantum-gravity-related approaches where the fundamental description of spacetime is not given by a classical smooth geometry. Despite their…
We investigate the effects of noncommutativity between the position-position, position-momentum and momentum-momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such noncommutativity…
In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum…
The axiomatic approach based on Wightman functions is developed in noncommutative quantum field theory. We have proved that the main results of the axiomatic approach remain valid if the noncommutativity affects only the spatial variables.
Cohomological Yang-Mills theory is formulated on a noncommutative differentiable four manifold through the $\theta$-deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the…
A noncommutative gauge theory is developed using a covariant star-product between differential forms defined on a symplectic manifold, considered as the space-time. It is proven that the field strength two-form is gauge covariant and…
In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al.. Here we extend it to certain noncommutative versions of the cylinder, $\mathbb{R}^{3}$ and…
Field theories on canonical noncommutative spacetimes, which are being studied also in connection with string theory, and on $\kappa$-Minkowski spacetime, which is a popular example of Lie-algebra noncommutative spacetime, can be naturally…
Introducing constant background fields into the noncommutative gauge theory, we first obtain a Hermitian fermion Lagrangian which involves a Lorentz violation term, then we generalize it to a new deformed canonical noncommutation relations…
We consider the noncommutative extension of the BF theory in two spacetime dimensions. We show that the introduction of the noncommutative parameter \theta_{\mu\nu}, already at first order in the analytical sector, induces infinitely many…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382, hep-th/0611160] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the…
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…
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…
We consider an easy way to get the noncommutative spacetime in Minkowski space. This corresponds to introducing a magnetic field ${\rm\bf B} = B \hat {\rm\bf k}$ in the plane. We construct a green's function in coordinate space which…
Constructing renormalizable models on non-commutative spaces constitutes a big challenge. Only few examples of renormalizable theories are known, such as the scalar Grosse-Wulkenhaar model. Gauge fields are even more difficult, since new…
We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincare) Lie algebra allows to construct a noncomutative…