International Journal of Theoretical Physics

, Volume 45, Issue 6, pp 1091-1106

First online:

Hamiltonian Formulation and Action Principle for the Lorentz-Dirac System

  • V. G. KupriyanovAffiliated withInstituto de Física, Universidade de São Paulo Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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