Eur. Phys. J. C (2007) 51: 229
https://doi.org/10.1140/epjc/s10052-007-0285-8

Regular Article - Theoretical Physics

Covariant realizations of kappa-deformed space

¹ Rudjer Bošković Institute, Bijenička c. 54, 10002, Zagreb, Croatia
² Faculty of Natural and Mathematical Sciences, Teslina 12, 21000, Split, Croatia

^* e-mail: meljanac@irb.hr

Received: 26 February 2007
Published online: 1 June 2007

Abstract

We study a Lie algebra type κ-deformed space with an undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. The space deformation depends on an arbitrary vector. Infinitely many covariant realizations in terms of commuting coordinates of undeformed space and their derivatives are constructed. The corresponding coproducts and star products are found and related in a new way. All covariant realizations are physically equivalent. Specially, a few simple realizations are found and discussed. The scalar fields, invariants and the notion of invariant integration is discussed in the natural realization.