Relations between positivity, localization and degrees of freedom: The Weinberg–Witten theorem and the van Dam–Veltman–Zakharov discontinuity

Abstract

The problem of accounting for the quantum degrees of freedom in passing from massive higher-spin potentials to massless ones, and the inverse problem of “fattening” massless tensor potentials of helicity ±h to their massive s=|h| counterparts, are solved – in a perfectly ghost-free approach – using “string-localized fields”.This approach allows to overcome the Weinberg–Witten impediment against the existence of massless |h|≥2 energy–momentum tensors, and to qualitatively and quantitatively resolve the van Dam–Veltman–Zakharov discontinuity concerning, e.g., very light gravitons, in the limit m→0.