Abstract
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.
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Kupriyanov, V.G. Hamiltonian Formulation and Action Principle for the Lorentz-Dirac System. Int J Theor Phys 45, 1091–1106 (2006). https://doi.org/10.1007/s10773-006-9112-5
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DOI: https://doi.org/10.1007/s10773-006-9112-5