TL;DR
This paper derives an exact two-component Runge-Lenz vector as a conserved quantity in a two-particle Chern-Simons electrodynamics system, revealing modified Poisson brackets with central charges.
Contribution
It introduces a novel derivation of the Runge-Lenz vector in a planar Chern-Simons electromagnetic context, extending classical conserved quantities to this framework.
Findings
Exact Runge-Lenz vector obtained for a two-particle system
Poisson brackets modified by central charges involving e e
Conserved quantities in Chern-Simons electrodynamics
Abstract
Following Dahl's method an exact Runge-Lenz vector M with two components M and M is obtained as a constant of motion for a two particle-system with charges e and e whose electromagnetic interaction is based on Chern-Simons electrodynamics. The Poisson bracket {M, M} = L but is modified by the appearance of the product e e as central charges.
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