Equations for the Electromagnetic Field Invariant Under the Galilean Group

Abstract

It is known that Maxwell’s electrodynamics is essentially a relativistic theory, and therefore the title of the present chapter may seem rather strange. However, we have already seen (see Chapter 7) that various subsystems of Maxwell’s equations possess symmetry relative to Galilean transformations. It turns out that there are also other systems of equations for the vectors E and H which include the first pair of Maxwell equations and are invariant under the Galilean group. Interest in such equations (which have been analyzed in the works of Levi-Leblond [138, 140, 141]) is due to the fact that investigation of recent years [37, 38, 40, 72] have shown that many problems of the interaction of a particle having spin with an external electromagnetic field can be successfully solved within the framework of a theory invariant under the Galilean group.