# Where Infinite Spin Particles Are Localizable

May 07, 2015

Particles states transforming in one of the infinite spin representations of
the Poincar\'e group (as classified by E. Wigner) are consistent with
fundamental physical principles, but local fields generating them from the
vacuum state cannot exist. While it is known that infinite spin states
localized in a spacelike cone are dense in the one-particle space, we show here
that the subspace of states localized in any double cone is trivial. This
implies that the free field theory associated with infinite spin has no
observables localized in bounded regions. In an interacting theory, if the
vacuum vector is cyclic for a double cone local algebra, then the theory does
not contain infinite spin representations. We also prove that if a
Doplicher-Haag-Roberts representation (localized in a double cone) of a local
net is covariant under a unitary representation of the Poincar\'e group
containing infinite spin, then it has infinite statistics.
These results hold under the natural assumption of the Bisognano-Wichmann
property, and we give a counter-example (with continuous particle degeneracy)
without this property where the conclusions fail. Our results hold true in any
spacetime dimension s+1 where infinite spin representations exist, namely s >
1.

Keywords:

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