Massless particles of high spin

Abstract

The existence of a Lorentz-covariant energy-momentum tensor in a quantum field theory has certain strong implications about the matrix elements of this Lorentz tensor between one-particle states of high-spin ($j\ensuremath{\ge}\frac{3}{2}$) zero-mass particles, composite or elementary. A similar result obtains for theories with a Lorentz-covariant current for zero-mass particles, composite or elementary with spin $j\ensuremath{\ge}1$. If these results are taken together with a continuity requirement on the matrix elements of the energy-momentum tensor and the current, respectively, one ends with a contradiction which can be removed only by assuming that such particles do not exist. We reexamine this conclusion and recognize that theories of higher-spin free particles are consistent but the continuity of the matrix elements do not obtain. The reason is traced to the abrupt change in the sign of the polarization when the momentum transfer changes from spacelike to null values. In the general case with particles of $j\ensuremath{\ge}\frac{3}{2}$ and $j\ensuremath{\ge}1$, respectively, we prove that the divergence of any tensor and any vector vanish between one-particle states.