Massless fields with integer spin

Abstract

The Fierz-Pauli Lagrangian for massive particles with arbitrary integral spin $s$, first obtained by Hagen and Singh, is examined in the limit of vanishing mass. Unexpectedly, a considerable simplification occurs. The potential $h$ is a symmetric tensor of rank $s$; the "trace" ${h}^{\ensuremath{'}}$, obtained by contraction of a pair of indices against the flat-space metric, does not vanish but the trace ${h}^{\ensuremath{'}\ensuremath{'}}$ of ${h}^{\ensuremath{'}}$ does. The wave equation admits a gauge group, and this implies conditions on the source. The divergence of the source need not vanish, only the traceless projection of the divergence must be zero; this is a major departure from the usual assumption and may bear on the question of the existence of a physically interesting source for fields with spin \ensuremath{\ge}3. This weaker condition on the source is sufficient to guarantee that only $\mathrm{helicities}\ifmmode\pm\else\textpm\fi{}s$ are transmitted between sources. A generalized Gupta program is proposed, that is, a search for a scheme for generating a theory of interacting, massless particles, consistent to all orders in the coupling constant.