International Journal of Theoretical Physics

, Volume 45, Issue 6, pp 1091–1106

Hamiltonian Formulation and Action Principle for the Lorentz-Dirac System


DOI: 10.1007/s10773-006-9112-5

Cite this article as:
Kupriyanov, V.G. Int J Theor Phys (2006) 45: 1091. doi:10.1007/s10773-006-9112-5


The possibility of constructing a Lagrangian and Hamiltonian formulation is examined for a radiating point-like charge usually described by the classical Lorentz-Dirac equation. It turns out that the latter equation cannot be obtained from the variational principle, and, furthermore, has nonphysical solutions. It is proposed to consider a physically equivalent set of reduced equations which admit a Hamiltonian formulation with non-canonical Poisson brackets. As an example, the effective dynamics of a non-relativistic particle moving in a homogeneous magnetic field is considered. The proposed Hamiltonian formulation may be considered as a first step to a consistent quantization of the Lorentz-Dirac system.

Key Words

Lorentz-Dirac equation systems with higher derivatives 

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrazil

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