Symmetries in Non Commutative Configuration space

Abstract

Extending earlier work(*), we examine the deformation of the canonical symplectic structure in a cotangent bundle $T^\star(\Q)$ by additional terms implying the Poisson non-commutativity of both configuration and momentum variables. In this short note, we claim this can be done consistently when $\Q$ is a Lie group. -- (*) F.J.Vanhecke, C.Sigaud and A.R.da Silva, arXiv:math-phys/0502003(2005) and Braz.J.Phys.{\bf 36},no IB,194(2006)

comunicated at the $V^{th}$ International Conference on Mathematical Methods in Physics -IC2006, april 2006, CBPF, Rio de Janeiro, at the First Latin American Conference on Lie Groups in Geometry, june 2006, Campinas and at the $XXVI{I}^{th}$ National Meeting of Particle Physicds and Field Theory, september 2006, Águas de Lindóia, Sâo Paulo