Related papers: Non-commutative waves for gravitational anyons
A full (triangular) quantum deformation of so(3,2) is presented by considering this algebra as the conformal algebra of the 2+1 dimensional Minkowskian spacetime. Non-relativistic contractions are analysed and used to obtain quantum Hopf…
The issue of how to deal with the modular transformations -- large diffeomorphisms -- in (2+1)-quantum gravity on the torus is discussed. I study the Chern-Simons/connection representation and show that the behavior of the modular…
The aim of these notes is to give an accessible and self-contained introduction to the theory of gravitational waves as the theory of a relativistic symmetric tensor field in a Minkowski background spacetime. This is the approach of a…
The connection between space-time covariant representations (obtained by inducing from the Lorentz group) and irreducible unitary representations (induced from Wigner's little group) of the Poincar\'{e} group is re-examined in the massless…
We analyze the elements characterizing the theory of induced representations of Lie groups, in order to generalize it to quantum groups. We emphasize the geometric and algebraic aspects of the theory, because they are more suitable for…
We continue the program, presented in previous Symposia, of discretizing physical models. In particular we calculate the integral Lorentz transformations with the help of discrete reflection groups, and use them for the covariance of…
Extended particles are considered in terms of the fields on the Poincar\'{e} group. Dirac like wave equations for extended particles of any spin are defined on the various homogeneous spaces of the Poincar\'{e} group. Free fields of the…
The group theoretical approach to the relativistic wave equations on the real reducible spaces for spin~0, 1/2 and~1 massless particles is considered. The invariant wave equations which determine the appropriate irreducible representations…
In relativistic quantum constraint mechanics the state of a physical system is constrained to a 3-dimensional subspace of Minkowski 4-space. Fourier transformation can be used to relate this state between constraint spaces in 4-position and…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
In this study, we construct a 1+1-dimensional, relativistic, free, complex scalar Quantum Field Theory on the noncommutative spacetime known as lightlike $\kappa$-Minkowski. The associated $\kappa$-Poincar\'e quantum group of isometries is…
We attempt to reconstruct the irreducible unitary representations of the Banach Lie group $U_0(\H)$ of all unitary operators $U$ on a separable Hilbert space $\H$ for which $U-{\mathbb I}$ is compact, originally found by Kirillov and…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
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)…
The description of the phase space of relativistic particles coupled to three-dimensional Einstein gravity requires momenta which are coordinates on a group manifold rather than on ordinary Minkowski space. The corresponding field theory…
We shall outline two ways of introducing the modification of Einstein's relativistic symmetries of special relativity theory - the Poincar\'{e} symmetries. The most complete way of introducing the modifications is via the noncocommutative…
We present two different quantum deformations for the (anti)de Sitter algebras and groups. The former is a non-standard (triangular) deformation of SO(4,2) realized as the conformal group of the (3+1)D Minkowskian spacetime, while 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…
Geometrical applications of the non-compact form of Cartan's exceptional Lie group G(2) is considered. This group generates specific rotations of 7-dimensional Minkowski-like space with three extra time-like coordinates and in some limiting…
The role of the quantum universal enveloping algebras of symmetries in constructing non-commutative geometry of the space-time including vector bundles, measure, equations of motion and their solutions is discussed. In the framework of the…