Differential structure on kappa-Minkowski space, and kappa-Poincare algebra

Details Differential structure on kappa-Minkowski space, and kappa-Poincare algebra Differential structure on kappa-Minkowski space, and kappa-Poincare algebra

2010-04-26

arxiv.org/abs/1004.4647v2

Int. J. Mod. Phys. A 26 (20) (2011), 3385-3402

Physics

Mathematical Physics

20 pages. Accepted for publication in International Journal of Modern Physics A

Scientific paper

We construct realizations of the generators of the $\kappa$-Minkowski space and $\kappa$-Poincar\'{e} algebra as formal power series in the $h$-adic extension of the Weyl algebra. The Hopf algebra structure of the $\kappa$-Poincar\'{e} algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on $\kappa$-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 $\kappa$-Minkowski space.

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