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A Note On Galilean Invariants In Semi-Relativistic Electromagnetism

The incompatibility between the Lorentz invariance of classical electromagnetism and the Galilean invariance of continuum mechanics is one of the major barriers to prevent two theories from merging. In this note, a systematic approach of obtaining Galilean invariant field variables and equations of electromagnetism within the semi-relativistic limit is reviewed and extended. In particular, the Galilean invariant forms of Poynting's theorem and the momentum identity, two most important electromagnetic identities in the thermomechanical theory of continua, are presented. In this note, we also introduce two frequently used stronger limits, namely the magnetic and the electric limit. The reduction of Galilean invariant variables and equations within these stronger limits are discussed.