Differential Structure on κ-MINKOWSKI Space, and κ-POINCARÉ Algebra
Abstract
We construct realizations of the generators of the κ-Minkowski space and κ-Poincaré algebra as formal power series in the h-adic extension of the Weyl algebra. The Hopf algebra structure of the κ-Poincaré algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on κ-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the κ-Minkowski space.
- Publication:
-
International Journal of Modern Physics A
- Pub Date:
- 2011
- DOI:
- 10.1142/S0217751X11053948
- arXiv:
- arXiv:1004.4647
- Bibcode:
- 2011IJMPA..26.3385M
- Keywords:
-
- κ-Minkowski space;
- κ-Poincaré algebra;
- realizations;
- differential forms;
- 02.20.Sv;
- 02.20.Uw;
- 02.40.Gh;
- Lie algebras of Lie groups;
- Quantum groups;
- Noncommutative geometry;
- Mathematical Physics;
- High Energy Physics - Theory
- E-Print:
- 20 pages. Accepted for publication in International Journal of Modern Physics A