Abstract
The equation of motion of a spinless quantum particle in an external uniform parallel electromagnetic field is derived from the symmetry of the field by group theoretical techniques. The minimal coupling is obtained directly, without a detour via the free particle equation. This derivation, which is valid in a Galilean as well as in a Poincare framework, is a contribution to the recasting process of quantum mechanics in the spirit of a paper by Levy-Leblond (1975).
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