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

The problem of accounting for the quantum degrees of freedom in passing from massive higher-spin potentials to massless ones and its inverse, the “fattening” of massless tensor potentials of helicity $\pm h$ to their massive $s=\mathrm{\mid }h\mathrm{\mid }$ 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 $\mathrm{\mid }h\mathrm{\mid }\ge 2$ energy-momentum tensors, and to qualitatively and quantitatively resolve the van Dam-Veltman-Zakharov discontinuity concerning, e.g., very light gravitons, in the limit $m\to 0$.