MG14 - Talk detail

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Abstract

Particles states transforming in one of the infinite spin representations of the Poincaré group (as classified by E. Wigner) are consistent with fundamental physical principles, but local fields generating them from the vacuum state cannot exist. It is known that infinite spin states localized in a spacelike cone are dense in the one-particle space. In this talk we show 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. If a Doplicher-Haag-Roberts representation of a local net is covariant under a unitary representation of the Poincaré group containing infinite spin, then it has infinite statistics. These results hold under the natural assumption of the Bisognano-Wichmann property, and, time permitting, we present 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.

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