``Good Propagation'' Constraints on Dual Invariant Actions in Electrodynamics and on Massless Fields

We present some consequences of non-anomalous propagation requirements on various massless fields. Among the models of nonlinear electrodynamics we show that only Maxwell and Born-Infeld also obey duality invariance. Separately we show that, for actions depending only on the $F_{\text{mn}}^2$ invariant, the permitted models have $L\sim \sqrt{1+F^2}$. We also characterize acceptable vector-scalar systems. Finally we find that wide classes of gravity models share with Einstein the null nature of their characteristic surfaces.