Remarks on the Electromagnetic Interactions of Massless Particles

A result recently obtained by Case and Gasiorowicz, that a massless particle of spin $s>\mathrm{}\frac{1}{2}$ cannot have the usual type of coupling to the electromagnetic field, is examined from a point of view different from that taken by those authors. It is shown that such a particle may, in fact, have derivative couplings of order $2s+1$ or $2s-1$ with the electromagnetic field for $s$ an integer or half-integer, respectively. These couplings cannot be generated by the usual requirement that the equations of motion be invariant under phase transformations, nor can they be present for dimensional reasons in a theory which contains no mass (or characteristic length), these conditions leading to the stated result. However, there is no reason in principle to expect such couplings to be absent if the massless particle interacts also with a charged massive field. An example is given for $s=1\mathrm{}$, and the cross section for Coulomb scattering of a massless particle is given for arbitrary $s$.