Related papers: Quantum groups and noncommutative spacetimes with …
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the…
We compare two versions of deformed dispersion relations (energy vs momenta and momenta vs energy) and the corresponding time delay up to the second order accuracy in the quantum gravity scale (deformation parameter). A general framework…
A contribution of quantum vacuum to the energy momentum tensor is inevitably experienced in the present universe. One requires the presence of non-zero cosmological constant ($\Lambda$) to make the various observations consistent. A case of…
We use factorisations of the local isometry groups arising in 3d gravity for Lorentzian and Euclidean signatures and any value of the cosmological constant to construct associated bicrossproduct quantum groups via semidualisation. In this…
The theory of quantum gravity, in which tetrads emerge as the bilinear combinations of the fermionic field, suggests that in general relativity the interval $ds$ is dimensionless. Several other approaches to quantum gravity, including the…
The quantum analogs of the N-dimensional Cayley-Klein spaces with different combinations of quantum and Cayley-Klein structures are described for non-minimal multipliers, which include the first and the second powers of contraction…
The spacetime short-distance structure at the Planck scale is governed by the Planck length, usually interpreted as a three-dimensional Euclidian length. As such, it is not Lorentz invariant and clashes with Einstein's special relativity,…
The existence of a non-zero cosmological constant $\Lambda$ gives rise to controversial interpretations. Is $\Lambda$ a universal constant fixing the geometry of an empty universe, as fundamental as the Planck constant or the speed of light…
We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to…
We propose a new approach to understand hierarchy problem for cosmological constant in terms of considering noncommutative nature of space-time. We calculate that vacuum energy density of the noncommutative quantum field theories in…
We provide a self-contained introduction to the quantum group approach to noncommutative geometry as the next-to-classical effective geometry that might be expected from any successful quantum gravity theory. We focus particularly on a…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
In the groupoid approach to noncommutative quantization of gravity, gravitational field is quantized in terms of a C*-algebra A of complex valued funcions on a groupoid G (with convolution as multiplication). In the noncommutative quantum…
The star product technique translates the framework of local fields on noncommutative space-time into nonlocal fields on standard space-time. We consider the example of fields on $\kappa$- deformed Minkowski space, transforming under…
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…
We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant) and is invariant under the…
We study a spatial-temporal structure of quantum fluctuations in the stress-energy tensor of zero-point modes for a scalar field in order to formulate a covariant model. The model describes an invariant vacuum contribution to the…
Quantum field planes furnish a noncommutative differential algebra $\Omega$ which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data required in their construction come from a quantum field…
We study the effect of the non-commutativity on the creation of scalar particles from vacuum in the anisotropic universe space-time. We derive the deformed Klein-Gordon equation up to second order in the non-commutativity parameter using…