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

Abstract

The model of kappa-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 on the coordinate algebra of kappa-deformed Euclidean space. We introduce a differential calculus with two interesting sets of one-forms and higher-order forms. The transformation law of vector fields is constructed in accordance with the transformation behaviour of derivatives. The crucial property of the different derivatives, forms and vector fields is that in an n-dimensional spacetime there are always n of them. This is the key difference with respect to conventional approaches, in which the differential calculus is (n+1)-dimensional. This work shows that derivative-valued quantities such as derivative-valued vector fields appear in a generic way on noncommutative spaces.

25 pages, footnotes and other small changes added

References in corpus (13)

• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Gauge Theory on Noncommutative Spaces
• Quantum $\kappa$-Poincare in Any Dimensions
• Deformed Field Theory on kappa-spacetime
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• Gauge theories on the kappa-Minkowski spacetime
• The Quantum Deformed Dirac Equation from the k-Poincare` Algebra
• Generalized Weyl systems and kappa-Minkowski space
• Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations
• The classical basis for $\kappa$-deformed Poincaré (super)algebra and the second $\kappa$-deformed supersymmetric Casimir
• Generalized kappa-Deformations and Deformed Relativistic Scalar Fields on Noncommutative Minkowski Space

Cited by in corpus (34)

• Kappa-Minkowski space-time and the star product realizations
• Twisted Statistics in kappa-Minkowski Spacetime
• Covariant realizations of kappa-deformed space
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Electrodynamics on $\kappa$-Minkowski space-time
• On $\kappa$-Deformation and UV/IR Mixing
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Generalized kappa-deformed spaces, star-products, and their realizations
• Geodesic equation in $k$-Minkowski spacetime
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Noncommutative Differential Forms on the kappa-deformed Space
• Newton's Equation on the kappa space-time and the Kepler problem
• $\kappa$-deformed Dirac Equation
• On kappa-deformation and triangular quasibialgebra structure
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Gauge theories on quantum spaces
• Effects of Noncommutativity on the Black Hole Entropy
• U(1) gauge field theory on kappa-Minkowski space
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• A symmetry invariant integral on kappa-deformed spacetime
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Gauge Theories on Deformed Spaces
• Noncommutative Field Theory on Homogeneous Gravitational Waves
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Deformed conformal and super-Poincaré symmetries in the non-(anti)commutative spaces
• Dimensional flow in the kappa-deformed space-time
• Effect of Non-commutativity of space-time on Thermodynamics of Photon gas
• Some considerations on duality concerning kappa-Minkowski spacetime theories