Relativistic Lagrangians for the Lorentz-Dirac equation

Abstract

We present two types of relativistic Lagrangians for the Lorentz-Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz-Dirac equation with a source-like term.

arXiv comment16 pages, a gauge transformation is considered, published version

References in corpus (6)

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• The dynamics of a charged particle
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Cited by in corpus (1)

• Quantization of the damped harmonic oscillator based on a modified Bateman Lagrangian