Helicity decoupling in the massless limit of massive tensor fields

Jens Mund, Karl-Henning Rehren, Bert Bert Schroer


Massive and massless potentials play an essential
role in the perturbative formulation of particle interactions. Many
difficulties arise due to the indefinite metric in gauge theoretic
approaches, or the increase with the spin of the UV dimension of
massive potentials. All these problems can be evaded in one stroke:
modify the potentials by suitable terms that leave unchanged the field
strengths, but are not polynomial in the momenta. This feature
implies a weaker localization property: the potentials are
``string-localized''. In this setting, several old issues can be
solved directly in the
physical Hilbert space of the respective particles: We construct
\set s for massless fields of any helicity (thus
evading the Weinberg-Witten theorem). We can control the separation
of helicities in the massless limit of higher spin fields and
conversely we recover massive potentials with $2s+1$ degrees of
freedom by a smooth deformation of the massless potentials
(``fattening''). We arrive at a simple understanding of the van
Dam-Veltman-Zakharov discontinuity concerning, e.g., the distinction
between a massless or a very light graviton. Finally, the
use of string-localized fields opens new perspectives for
interacting quantum field theories with, e.g., vector bosons
or gravitons.

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