A non-commutative Minkowskian spacetime from a quantum AdS algebra

Abstract

A quantum deformation of the conformal algebra of the Minkowskian spacetime in $(3+1)$ dimensions is identified with a deformation of the $(4+1)$-dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are explicitly obtained, and the former coincides with the well known $\kappa$-Minkowski space. Next, by working in the conformal basis, a new non-commutative Minkowskian spacetime is constructed through the full (all orders) dual quantum group spanned by deformed Poincar\'e and dilation symmetries. Although Lorentz invariance is lost, the resulting non-commutative spacetime is quantum group covariant, preserves space isotropy and, furthermore, can be interpreted as a generalization of the $\kappa$-Minkowski space in which a variable fundamental scale (Planck length) appears.Comment: Revised version accepted for pubblication on PLB. Latex file, 9 page

On 3+1 Anti-de Sitter and de Sitter Lie Bialgebras with Dimensionful Deformation Parameters

“…Nevertheless, further corrections depending on ω can be expected to appear in the complete quantum (A)dS spaces similarly to what happens in the 2+1 case [11].…”

“…Hence this point could be checked once the complete quantum algebra and the dual (all-orders) non-commutative spacetime were obtained. In this respect, see [12] for an explicit example where a new non-commutative Minkowskian spacetime associated to a quantum Weyl-Poincaré algebra is shown to be covariant under quantum group transformations.…”

BRAIDED STATISTICS FROM ABELIAN TWIST IN Κ-Minkowski SPACETIME

“…We start from the undeformed bosonic commutation relation and arrive at deformed relations (16) and (17) in terms of universal R matrix.…”

“…To understand κ-MST more deeply, twist formalism such as Jordanian twist [13,14,15], κ-like deformation of quantum Weyl and conformal algebra [16] and the light-cone κ-deformation of Poincaré algebra [17] has been tried. In the following, abelian twist in [18,19,20] will be used.…”

Analytical Solutions to the Klein–Gordon Equation with Position-Dependent Mass for q -Parameter Pöschl–Teller Potential

“…Quantum deformation [41] has received much attentions because of its relation with applications in nuclei [42][43][44][45], statistical-quantum theory, string/brane theory and conformal field theory [46][47][48][49]. Recently, some authors have been introduced some potentials in terms of hyperbolic functions in the view of q-deformation [50].…”