A Noncommutative Minkowskian space-time from a quantum AdS algebra
Jun, 2003
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Abstract:
A quantum deformation of the conformal algebra of the Minkowskian spacetime in dimensions is identified with a deformation of the -dimensional AdS algebra. Both Minkowskian and AdS first-order non-commutative spaces are explicitly obtained, and the former coincides with the well known -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 -Minkowski space in which a variable fundamental scale (Planck length) appears.Note:
- Revised version accepted for pubblication on PLB. Latex file, 9 pages
- 02.20.Uw
- 11.30.-j
- 04.60.-m
- Quantum algebras
- Deformation
- Minkowski
- Anti-de Sitter
- Poincaré
- Non-commutative spacetime
- algebra: conformal
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