String-Localized Free Vector and Tensor Potentials for Massive Particles with Any Spin: I. Bosons

Abstract

It is well-known that a (point-localized) free quantum field for massive particles with spin $s$ acting in a Hilbert space has at best scaling dimension $s+1$, which excludes its use in the perturbative construction of renormalizable interacting models for higher spin ($s\geq 1$). Up to date, such models have been constructed only in the context of gauge theory, at the cost of introducing additional unphysical (ghost) fields and an unphysical (indefinite metric) state space. The unphysical degrees of freedom are divided out by requiring gauge (or BRST) invariance. We construct free quantum fields for higher spin particles which have the same good UV behaviour as the scalar field (scaling dimension one), and at the same time act on a Hilbert space without ghosts. They are localized on semi-infinite strings extending to space-like infinity, but are linearly related to their point-local counterparts. We argue that this is sufficient locality for a perturbative construction of interacting models of the gauge theory type, with a string-independent S-matrix and point-localized interacting observable fields. The usual principle of gauge-invariance is here replaced by the (deeper) principle of locality.