Communications in Mathematical Physics

, Volume 315, Issue 2, pp 465–488 | Cite as

Braid Group Statistics Implies Scattering in Three-Dimensional Local Quantum Physics

Article

Abstract

It is shown that quantum fields for massive particles with braid group statistics (Plektons) in three-dimensional space-time cannot be free, in a quite elementary sense: They must exhibit elastic two-particle scattering into every solid angle, and at every energy. This also implies that for such particles there cannot be any operators localized in wedge regions which create only single particle states from the vacuum and which are well-behaved under the space-time translations (so-called temperate polarization- free generators). These results considerably strengthen an earlier “NoGo-theorem for ’free’ relativistic Anyons”.

As a by-product we extend a fact which is well-known in quantum field theory to the case of topological charges (i.e., charges localized in space-like cones) in d ≥ 4, namely: If there is no elastic two-particle scattering into some arbitrarily small open solid angle element, then the 2-particle S-matrix is trivial.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institut de Physique ThéoriqueCEASaclayFrance
  2. 2.Departamento de FísicaUniversidade Federal de Juiz de ForaJuiz de ForaBrazil

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