Generalized kappa-deformed spaces, star products and their realizations

Abstract

In this work we investigate generalized kappa-deformed spaces. We develop a systematic method for constructing realizations of noncommutative (NC) coordinates as formal power series in the Weyl algebra. All realizations are related by a group of similarity transformations, and to each realization we associate a unique ordering prescription. Generalized derivatives, the Leibniz rule and coproduct, as well as the star-product are found in all realizations. The starproduct and Drinfel'd twist operator are given in terms of the coproduct, and the twist operator is derived explicitly in special realizations. The theory is applied to a Nappi-Witten type of NC space.

Effect of non-commutativity of space-time on thermodynamics of photon gas

“…In this section, we give the brief summary of κ-deformed space-time [9][10][11][12][13], which is an example of a non-commutative space-time whose coordinates obey commutation relations,…”

“…The symmetry algebra of the underlying κ-space-time generated by M µν and D µ known as the undeformed κ-Poincare algebra. Their generators D µ and M µν obey [9][10][11][12][13]…”

“…Various aspects of physical models incorporating DSR where analysed in [6][7][8]. Doubly special relativity leads to study the κdeformed space-time [9][10][11][12][13] which is one of the example of non-commutative space-time and the corresponding symmetry algebra is deformed which is called the κ-Poincare algebra.…”

Superdense star in a spacetime with minimal length

“…In this work we will use this method where we expresses the non-commutative coordinates as a function of commutative coordinates, their derivatives and deformation parameter. Different realisations of non-commutative coordinates exist for κ-deformed space-time [27,28,29,30,31]. Here we have choosen a particular realisation for calculations.…”

Κ-Deformed DIRAC EQUATION

“…It has been shown in [8], that the symmetry algebra of the κ-deformed space-time is defined by the κ-Poincare algebra, which is a Hopf algebra. The symmetry algebra of the κ-deformed space-time can also be realised using undeformed κ-Poincare algebra, where the defining relations are same as that of the usual Poincare algebra, but then the explicit form of the generators are deformed [9][10][11][12][13].Various studies have been carried out analysing field theory models defined in κ-deformed spacetime [14][15][16][17][18][19][20][21][22][23][24]. In most of these studies, field equations, which are invariant under the symmetry algebra, defined in κ-deformed space-times are set up from the κ-deformed quadratic Casimir [9] of the algebra.…”