ON q-COVARIANT WAVE FUNCTIONS

Abstract

The differential realization of the recently proposed deformed Poincaré algebra is considered. The notion of covariant wave functions is introduced and their explicit form in the "minimal" (in Weinberg's sense) case is given. The deformed Dirac equation is constructed.

Untitled

“…It should be pointed out that the star product (32) is more physical, because the parameters p µ can be interpreted as the fourmomenta with the addition law derived from the κ-deformation of relativistic symmetries [11][12][13][14][15].…”

“…In this talk we will consider a particular example of so-called κ-deformation of space-time symmetries [11][12][13][14][15] with noncommutativity of space-time coordinates described by the following solvable Lie-algebraic relations:…”

Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

“…The first one has a deformed coproduct with exponential terms (it is just the (2+1) analogue of the deformation given in [34]). The latter presents a simpler deformation (with only linear non-primitive terms) and reproduces the deformation of boosts (4.12) in the non-relativistic case.…”

“…), and the Giller's (3+1) Galilei deformation [34] obtained by applying on the former the φ ε 2 contraction; note that the latter it is not a coboundary (see third row of table IV).…”

(2+1) Null-Plane Quantum Poincaré Group From a Factorized Universal R-Matrix

“…Two of them are obtained in a natural way within a purely kinematical framework encoded within the usual Poincaré basis. They are the well-known κ-Poincaré algebra [1,2] where the deformation parameter can be interpreted as a fundamental time scale and a q-Poincaré algebra [3] where the quantum parameter is a fundamental length. On the other hand, the remaining structure (the null-plane quantum Poincaré algebra recently introduced in [4,5]) strongly differs from the previous ones: firstly, it is constructed in a null-plane context where the Poincaré invariance splits into a kinematical and dynamical part [6] and, secondly, this case is a quantization of a non-standard (triangular) coboundary Lie bialgebra.…”