Lorentz transformations as Lie--Poisson symmetries

Journal Article · Sun Oct 01 00:00:00 EDT 1995 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531278· OSTI ID:240461

Simoni, A ^[1]; Stern, A; Yakushin, I ^[2]

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1. Dipto. di Scienze Fisiche, Universita di Napoli, 80125 Napoli (Italy)
2. Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487 (United States)

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{sub {ital q}}(2, {ital 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 particle trajectory and find that it originates and terminates at singularities. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

• DOE Contract Number: FG05-84ER40141
• OSTI ID: 240461
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 36; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
HAMILTONIAN FUNCTION
LIE GROUPS
LORENTZ GROUPS
LORENTZ TRANSFORMATIONS
SL GROUPS
SPACE-TIME
SYMMETRY GROUPS