Related papers: Noncommutative spaces of worldlines
Kappa-Minkowski space-time is an example of noncommutative space-time with potentially interesting phenomenological consequences. However, the construction of field theories on this space, although operationally well-defined, is plagued…
A noncommutative *-algebra that generalizes the canonical commutation relations and that is covariant under the quantum groups SOq(3) or SOq(1,3) is introduced. The generating elements of this algebra are hermitean and can be identified…
We study the Lie bialgebra structures that can be built on the one-dimensional central extension of the Poincar\'e and (A)dS algebras in (1+1) dimensions. These central extensions admit more than one interpretation, but the simplest one is…
When developing a quantum theory for a physical system, one determines the system's symmetry group and its irreducible unitary representations. For Minkowski space, the symmetry group is the Poincar\'e group, $\mathbb{R}^4 \rtimes…
We show that the $\kappa$-deformed Poincar\'e quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct $U(so(1,3))\cobicross T$. The algebra is a semidirect product of the classical Lorentz…
In the formulation of (2+1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincar\'e group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit…
A fully Poincare' covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincare' group, and thus complies with the original Wigner approach to quantum symmetries. This…
In this paper, we present the results of our investigation relating particle dynamics and non-commutativity of space-time by using Dirac's constraint analysis. In this study, we re-parameterise the time $t=t(\tau)$ along with $x=x(\tau)$…
In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates.…
The $\kappa$-deformation of the D-dimensional Poincar\'e algebra $(D\geq 2)$ with any signature is given. Further the quadratic Poisson brackets, determined by the classical $r$-matrix are calculated, and the quantum Poincar\'e group "with…
We discuss the construction of a free scalar quantum field theory on $\kappa$-Minkowski noncommutative spacetime. We do so in terms of $\kappa$-Poincar\'e-invariant $N$-point functions, i.e. multilocal functions which respect the deformed…
Stabilization, by deformation, of the Poincar\'{e}-Heisenberg algebra requires both the introduction of a fundamental lentgh and the noncommutativity of translations which is associated to the gravitational field. The noncommutative…
The classical $r$-matrix for $N=1$ superPoincar{\'e} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{\'e} supergroup. The standard correspondence principle between the…
Within the setting of a recently proposed model of quantum fields on noncommutative Minkowski spacetime, the consequences of the consistent application of the proper, untwisted Poincare group as the symmetry group are investigated. The…
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
The role of quantum universal enveloping algebras of symmetries in constructing a noncommutative geometry of space-time and corresponding field theory is discussed. It is shown that in the framework of the twist theory of quantum groups,…
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase…
Unified graded differential algebra, generated by $\kappa$-Minkowski noncommutative (NC) coordinates, Lorentz generators and anticommuting one-forms, is constructed. It is compatible with $\kappa$-Poincar\'e-Hopf algebra. For time- and…
We construct the full quantum algebra, the corresponding Poisson-Lie structure and the associated quantum spacetime for a family of quantum deformations of the isometry algebras of the (2+1)-dimensional anti-de Sitter (AdS), de Sitter (dS)…