Braid Group Statistics Implies Scattering in ThreeDimensional Local Quantum Physics
Abstract
It is shown that quantum fields for massive particles with braid group statistics (Plektons) in threedimensional spacetime cannot be free, in a quite elementary sense: They must exhibit elastic twoparticle 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 wellbehaved under the spacetime translations (socalled temperate polarization free generators). These results considerably strengthen an earlier "NoGotheorem for 'free' relativistic Anyons". As a byproduct we extend a fact which is wellknown in quantum field theory to the case of topological charges (i.e., charges localized in spacelike cones) in d ≥ 4, namely: If there is no elastic twoparticle scattering into some arbitrarily small open solid angle element, then the 2particle Smatrix is trivial.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 October 2012
 DOI:
 10.1007/s0022001215606
 arXiv:
 arXiv:1112.5785
 Bibcode:
 2012CMaPh.315..465B
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 81T05
 EPrint:
 25 pages, 4 figures. Comment on modelbuilding added in the introduction