In this paper, we derive Lorentz force and Maxwell's 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 non-commutative space-time. We also show the equivalence of minimal coupling prescription and Feynman's 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 non-commutativity. 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.

In this paper, we derive corrections to the geodesic equation due to the κ deformation of curved spacetime, 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-noncommutativity can be interpreted as an extra drag that acts on the particle while moving in this κ-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 κ-spacetime.

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-Poincaré 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. Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. 1450022-3 Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. 1450022-4 Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. 1450022-5 Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. 1450022-6 Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by UNIVERSITY OF TORONTO on 02/03/15. For personal use only. multiplication map defined by m ⋆1 . The property of right ideal J is m ⋆ (J ⊲ (f ⊗ g)) = 0. For the right ideals J 0 and J , we have J 0 (H ⊗ H) = J 0 , J (H ⊗ H) = J , J = F J 0 F −1 = F J 0 , J J 0 ⊂ J , J 0 J ⊂ J 0 .

Classification of differential forms on κ-Minkowski space, particularly, the classification of all bicovariant differential calculi of classical dimension is presented. By imposing super-Jacobi identities we derive all possible differential algebras compatible with the κ-Minkowski algebra for time-like, space-like and light-like deformations. Embedding into the super-Heisenberg algebra is constructed using non-commutative (NC) coordinates and one-forms. Particularly, a class of differential calculi with an undeformed exterior derivative and one-forms is considered. Corresponding NC differential calculi are elaborated. Related class of new Drinfeld twists is proposed. It contains twist leading to κ-Poincaré Hopf algebra for light-like deformation. Corresponding super-algebra and deformed super-Hopf algebras, as well as the symmetries of differential algebras are presented and elaborated. Using the NC differential calculus, we analyze NC field theory, modified dispersion relations, and discuss further physical applications.

In this paper the BTZ black hole geometry is probed with a noncommutative scalar field which obeys the κ-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton's constant due to the effects of the noncommutativity. 1