Relativistic Lagrangians for the Lorentz–Dirac equation

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 ad...

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Bibliographic Details
Published in:Annals of physics 2015-09, Vol.360, p.539-548
Main Authors: Deguchi, Shinichi, Nakano, Kunihiko, Suzuki, Takafumi
Format: Article
Language:English
Subjects:
Charged particle
CHARGED PARTICLES
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Lagrange multiplier
Lagrangian
LAGRANGIAN FUNCTION
Lorentz–Dirac equation
Parameter estimation
Quantum physics
Radiation reaction
RELATIVISTIC RANGE
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Summary: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.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2015.05.023