Lorentz Transformations as Lie-Poisson Symmetries

A. Simoni; A. Stern; I. Yakushin

doi:10.1063/1.531278

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arXiv · q-alg/9501026

Lorentz Transformations as Lie-Poisson Symmetries

A. Simoni·A. Stern·I. Yakushin

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Abstract

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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BibTeX RIS

A. Simoni, A. Stern, I. Yakushin. 1995-01-25. Lorentz Transformations as Lie-Poisson Symmetries. https://doi.org/10.1063/1.531278

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