Related papers: The Boosts in the Noncommutative Special Relativit…
We review an instance of noncommutative geometry based on a specific realization of the model of doubly special relativity proposed by Magueijo and Smolin (MS) on noncommutative spacetime. In particular, we discuss the Hopf algebra…
A covariant generalization of a non-relativistic stochastic quantum mechanics introduced by de la Pe\~na and Cetto is formulated. The analysis is done in space-time and avoids the use of a non-covariant time evolution parameter in order to…
We propose a nonstandard approach to solving the apparent incompatibility between the coalgebra structure of some inhomogeneous quantum groups and their natural complex conjugation. In this work we sketch the general idea and develop the…
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic…
We study the structure of maps that Lorentz boosts induce on the spin degree of freedom of a system consisting of two massive spin-$1/2$ particles. We consider the case where the spin state is described by the Werner state and the momenta…
Noncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum…
It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac…
The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter.…
We show that U(\infty) symmetry transformations of the noncommutative field theory in the Moyal space are generated by a combination of two W_{1+\infty} algebras in the Landau problem. Geometrical meaning of this infinite symmetry is…
The realization that forthcoming experimental studies, such as the ones planned for the GLAST space telescope, will be sensitive to Planck-scale deviations from Lorentz symmetry has increased interest in noncommutative spacetimes in which…
We develop a relativistic velocity space called \emph{rapidity space} from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-colinear Lorentz boosts.…
We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2+1 dimensions, motivated by its role as a deformed Poincar\'e symmetry and symmetry algebra in (2+1)-dimensional quantum gravity. We…
The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to…
This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…
In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in $R^{1,d-1}$ is investigated. The introduction of a new generator is…
A Gelfan'd--Dyson mapping is used to generate a one-boson realization for the non-standard quantum deformation of $sl(2,\R)$ which directly provides its infinite and finite dimensional irreducible representations. Tensor product…
In this article, matrix and vector formalisms for Lorentz transformations in time ($t$) and two space dimensions ($x$ and $y$) are developed and discussed. Lorentz transformations conserve the squared interval $t^2 - x^2 - y^2$. Examples of…
We study a family of noncommutative spacetimes constructed by one four-vector. The large set of coordinate commutation relations described in this way includes many cases that are widely studied in the literature. The Hopf-algebra…
We present two classes of examples of Hopf algebroids associated with noncommutative principal bundles. The first comes from deforming the principal bundle while leaving unchanged the structure Hopf algebra. The second is related to…
We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this…