Abstract

Using a distribution theory, a useful formula to obtain the most general classical relativistic equation of motion for an arbitrary multipole point particle, in an external electromagnetic field, in Minkowski space is derived. The formula is formally obtained from the singular solutions of Maxwell's equations and the definition of the energy-momentum tensor neglecting radiation reaction. As a particular application of this formula, the authors extract the general equation of motion for a point particle possessing up to quadrupole moments.

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