Canonical and Lie-algebraic twist deformations of Galilei algebra.pdfVIP

a r X i v : 0 8 0 1 .1 2 0 6 v 1 [ h e p - t h ] 8 J a n 2 0 0 8 Canonical and Lie-algebraic twist deformations of Galilei algebra Marcin Daszkiewicz Institute of Theoretical Physics University of Wroc law pl. Maxa Borna 9, 50-206 Wroc law, Poland e-mail: marcin@ift.uni.wroc.pl Abstract We describe various nonrelativistic contractions of two classes of twisted Poincare algebra: canonical one (θμν-deformation) and the one leading to Lie-algebraic mod- els of noncommutative space-times. The cases of contraction-independent and contraction-dependent twist parameters are considered. We obtain five models of noncommutative nonrelativistic space-times, in particular, two new Lie-algebraic nonrelativistic deformations of space-time, respectively, with quantum time/classical space and with quantum space/classical time. 1 1 Introduction In the last decade the interest in a class of theories describing kinematics different from Special Relativity is growing rapidly. The main reason for such type of considerations follows from many phenomenological suggestions, which state that relativistic space-time symmetries should be modified (deformed) at Planck scale, while the classical Poincare invariance still remains valid at larger distances [1]-[4]. There are also several formal ar- guments based mainly on quantum gravity [5], [6] and string theory [7], [8] indicating that space-time at Planck-length should be noncommutative, i.e. it should have a quantum nature. An important candidate for a modification of relativistic symmetry in ultra-high energy regime, so-called κ-deformed Poincare? algebra, has been proposed in the Hopf algebraic framework of quantum groups in [9], [10]. As a result of contraction of q-deformed anti- De-Sitter algebra one obtains κ-Poincare? group which leads to Lie-algebraic space-time noncommutativity, the κ-Minkowski space [11], [12], with the mass-like deformation pa- rameter κ. Besides, it also gives a formal framework for such theoretical const