Lie particle and its Batalin-Tyutin extension

In this Letter we have proposed a point particle model that generates a noncommutative three-space, with the coordinate brackets being Lie algebraic in nature, in particular isomorphic to the angular momentum algebra. The work is in the spirit of our earlier works in this connection, i.e., [S. Ghosh, P. Pal, Phys. Lett. B 618 (2005) 243, hep-th/0502192; S. Ghosh, Phys. Lett. B 623 (2005) 251, hep-th/0506084], where the κ-Minkowski form of noncommutative spacetime was considered. This nonlinear and operatorial nature of the configuration space coordinate algebra can pose problems regarding its quantization. This prompts us to embed the model in the Batalin-Tyutin extended space where the equivalent model comprises of phase space variables satisfying a canonical algebra. We also compare our present model with the point particle model, previously proposed by us, in the context of κ-Minkowski spacetime.