The exact Darwin Lagrangian

Abstract

Darwin (1920) noted that when radiation can be neglected it should be possible to eliminate the radiation degrees-of-freedom from the action of classical electrodynamics and keep the discrete particle degrees-of-freedom only. Darwin derived his well known Lagrangian by series expansion in $v/c$ keeping terms up to order $(v/c{)}^2$. Since radiation is due to acceleration the assumption of low speed should not be necessary. A Lagrangian is suggested that neglects radiation without assuming low speed. It cures deficiencies of the Darwin Lagrangian in the ultra-relativistic regime.

2.5 pages, no figures

References in corpus (9)

• Historical roots of gauge invariance
• From Lorenz to Coulomb and other explicit gauge transformations
• The Rest-Frame Darwin Potential from the Lienard-Wiechert Solution in the Radiation Gauge
• Small Effects in Astrophysical Fusion Reactions
• Darwin-Lagrangian Analysis for the Interaction of a Point Charge and a Magnet: Considerations Related to the Controversy Regarding the Aharonov-Bohm and Aharonov-Casher Phase Shifts
• Instantaneous fields in classical electrodynamics
• Long Range Magnetic Order and the Darwin Lagrangian
• Equilibrium correlations in charged fluids coupled to the radiation field
• What is the Force between Electrons?

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• Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas
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• Relativistic dynamical friction in stellar systems
• Vector Theory of Gravity
• On the nature of the plasma equilibrium