Covariant realizations of kappa-deformed space

Abstract

We study a Lie algebra type $\kappa$-deformed space with undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. 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.

31 pages, no figures, LaTeX

References in corpus (7)

• A Gravity Theory on Noncommutative Spaces
• Symmetry, Gravity and Noncommutativity
• New realizations of Lie algebra kappa-deformed Euclidean space
• Gauge theories on the kappa-Minkowski spacetime
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• $\kappa -$Minkowski spacetime and a uniformly accelerating observer
• Determinants and Inversion of Gram Matrices in Fock Representation of $\{q_{kl}\}$- Canonical Commutation Relations and Applications to Hyperplane Arrangements and Quantum Groups. Proof of an Extension of Zagier's Conjecture

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