Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-06-10
Phys.Lett. B574 (2003) 276-282
Physics
High Energy Physics
High Energy Physics - Theory
Revised version accepted for pubblication on PLB. Latex file, 9 pages
Scientific paper
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.
Ballesteros Angel
Bruno Nicola Rossano
Herranz Francisco J.
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