Tajron Jurić

Electrodynamics on

In this paper, we derive Lorentz force and Maxwells equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to noncommutative space-time. We also show the equivalence of minimal coupling prescription and Feynmans approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this noncommutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.

\kappa

The quantum phase space described by Heisenberg algebra possesses undeformed Hopf algebroid structure. The κ-deformed phase space with noncommutative coordinates is realized in terms of undeformed quantum phase space. There are infinitely many such realizations related by similarity transformations. For a given realization, we construct corresponding coproducts of commutative coordinates and momenta (bialgebroid structure). The κ-deformed phase space has twisted Hopf algebroid structure. General method for the construction of twist operator (satisfying cocycle and normalization condition) corresponding to deformed coalgebra structure is presented. Specially, twist for natural realization (classical basis) of κ-Minkowski space–time is presented. The cocycle condition, κ-Poincare algebra and R-matrix are discussed. Twist operators in arbitrary realizations are constructed from the twist in the given realization using similarity transformations. Some examples are presented. The important physical applications of twists, realizations, R-matrix and Hopf algebroid structure are discussed.

-Minkowski space-time

Abstract We unify κ -Poincare algebra and κ -Minkowski spacetime by embedding them into quantum phase space. The quantum phase space has Hopf algebroid structure to which we apply the twist in order to get κ -deformed Hopf algebroid structure and κ -deformed Heisenberg algebra. We explicitly construct κ -Poincare–Hopf algebra and κ -Minkowski spacetime from twist. It is outlined how this construction can be extended to κ -deformed super-algebra including exterior derivative and forms. Our results are relevant for constructing physical theories on noncommutative spacetime by twisting Hopf algebroid phase space structure.

Twists, realizations and Hopf algebroid structure of κ-deformed phase space

In this paper, we derive corrections to the geodesic equation due to the

κ-Poincaré–Hopf algebra and Hopf algebroid structure of phase space from twist

k

Geodesic equation in k-Minkowski spacetime.

-deformation of curved space-time, up to the first order in the deformation parameter a. This is done by generalizing the method from our previous paper [31], to include curvature effects. We show that the effect of

Κ-Deformed Phase Space, Hopf Algebroid and Twisting

k

Differential forms and κ-Minkowski spacetime from extended twist

-noncommutativity can be interpreted as an extra drag that acts on the particle while moving in this

Realizations of

k

\kappa

-deformed curved space. We have derived the Newtonian limit of the geodesic equation and using this, we discuss possible bounds on the deformation parameter. We also derive the generalized uncertainty relations valid in the non-relativistic limit of the