Canonical and Lie-Algebraic Twist Deformations of Galilei Algebra

Abstract

We describe various nonrelativistic contractions of two classes of twisted Poincare algebra: canonical one (θ µν -deformation) and the one leading to Lie-algebraic models 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.

The Henon--Heiles System Defined on Canonically Deformed Space-time

“…2 It should be noted that in accordance with the Hopf-algebraic classification of all deformations of relativistic and nonrelativistic symmetries (see references [13], [14]), apart of canonical [10]- [12] space-time noncommutativity, there also exist Lie-algebraic [12]- [17] and quadratic [12], [17]- [19] type of quantum spaces.…”

“…In this section we very shortly recall the basic facts associated with the (twisted) canonically deformed Galilei Hopf algebra U θ (G) and with the corresponding quantum spacetime [12]. Firstly, it should be noted that in accordance with Drinfeld twist procedure [20] the algebraic sector of Hopf structure U θ (G) remains undeformed…”

“…[8], [9]). In this article we investigate the impact of the well-known (simplest) canonically deformed Galilei space-time [10]- [12] 1 ,…”

“…In second Section we briefly remaind the basic properties of classical Henon-Heiles system. In Section 3 we recall canonical noncommutative quantum Galilei space-time proposed in article [12]. Section 4 is devoted to the new canonically deformed Henon-Heiles model while the conclusions are discussed in Final remarks.…”

The Henon–Heiles system defined on Lie-algebraically deformed Galilei spacetime

“…Our aim in this paper is to study further the impact of noncommutative generalization of the model on its chaotic properties. Recently, there has been proposed in article [11] the noncommutative counterpart of Henon-Heiles system defined on the following canonically deformed Galilei space-time [12]- [14] 1 ,…”