Lorentz Transformations as Lie-Poisson Symmetries

Details Lorentz Transformations as Lie-Poisson Symmetries Lorentz Transformations as Lie-Poisson Symmetries

1995-01-25

arxiv.org/abs/q-alg/9501026v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

10.1063/1.531278

We write down the Poisson structure for a relativistic particle where the Lorentz group does not act canonically, but instead as a Poisson-Lie group. In so doing we obtain the classical limit of a particle moving on a noncommutative space possessing $SL_q(2,C)$ invariance. We show that if the standard mass shell constraint is chosen for the Hamiltonian function, then the particle interacts with the space-time. We solve for the trajectory and find that it originates and terminates at singularities.

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