Non-relativistic limits of Maxwell's equations

Abstract

In 1973, Le Bellac and Levy-Leblond (Nuovo Cimento B 14, 217-234) discovered that Maxwell's equations possess two non-relativistic Galilei-covariant limits, corresponding to E >> cB (electric limit) or E << cB (magnetic limit). Here, we provide a systematic, yet simple, derivation of these two limits based on a dimensionless form of Maxwell's equations and an expansion of the electric and magnetic fields in a power series of some small parameters. Using this procedure, all previously known results are recovered in a natural and unambiguous way. Some further extensions are also proposed.

References in corpus (5)

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• On some applications of Galilean electrodynamics of moving bodies
• The Galilean limits of Maxwell's equations
• The covariant formulation of Maxwell's equations expressed in a form independent of specific units
• From self-consistent covariant effective field theories to their Galilean-invariant counterparts

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