Where Infinite Spin Particles are Localizable
Abstract
Particle 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. While it is known that infinite spin states localized in a spacelike cone are dense in the oneparticle 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 DoplicherHaagRoberts representation (localized in a double cone) 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 BisognanoWichmann property, and we give a counterexample (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≥ 2}.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 July 2016
 DOI:
 10.1007/s0022001524759
 arXiv:
 arXiv:1505.01759
 Bibcode:
 2016CMaPh.345..587L
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Operator Algebras;
 81Txx;
 46L60
 EPrint:
 v2: additional material to make it more selfcontained, references added. v3: Proof of Prop. 8.4 fixed