# Covariant realizations of kappa-deformed space

@article{Meljanac2007CovariantRO, title={Covariant realizations of kappa-deformed space}, author={Stjepan Meljanac and Sa{\vs}a Kre{\vs}i{\'c}–Juri{\'c} and Marko Stoji{\'c}}, journal={The European Physical Journal C}, year={2007}, volume={51}, pages={229-240} }

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…

## 91 Citations

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The κ-Minkowski spacetime and Lorentz algebra are unified in unique Lie algebra. Introducing commutative momenta, a family of κ-deformed Heisenberg algebras and κ-deformed Poincare algebras are…

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## References

SHOWING 1-10 OF 63 REFERENCES

New realizations of Lie algebra kappa-deformed Euclidean space

- Mathematics
- 2006

We study Lie algebra κ-deformed Euclidean space with undeformed rotation algebra SOa(n) and commuting vectorlike derivatives. Infinitely many realizations in terms of commuting coordinates are…

A gravity theory on noncommutative spaces

- Mathematics
- 2005

A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter ?. The algebraic relations remain the same, whereas the…

Deformed field theory on $\kappa$-spacetime

- Mathematics, Physics
- 2003

Abstract.A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (the Poincaré…

Derivatives, forms and vector fields on the κ-deformed Euclidean space

- Mathematics
- 2004

The model of κ-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper, we present new results concerning different sets of derivatives…

Gauge theories on the $\kappa$-Minkowski spacetime

- Mathematics, Physics
- 2003

Abstract.This study of gauge field theories on $\kappa$-deformed Minkowski spacetime extends previous work on field theories on this example of a non-commutative spacetime. We construct deformed…

New Lie-algebraic and quadratic deformations of Minkowski space from twisted Poincaré symmetries

- Mathematics
- 2006

Bicrossproduct structure of κ-Poincare group and non-commutative geometry

- Mathematics, Physics
- 1994

Deformed symmetry in Snyder space and relativistic particle dynamics

- Mathematics
- 2006

We describe the deformed Poincare-conformal symmetries implying the covariance of the noncommutative space obeying Snyder's algebra. Relativistic particle models invariant under these deformed…

Local field theory on κ-Minkowski space, star products and noncommutative translations

- Mathematics
- 2000

We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over κ-Minkowski space and κ-deformed…