Fractional helicity, Lorentz symmetry breaking, compactification and anyons
Abstract
We construct the covariant, spinor sets of relativistic wave equations for a massless field on the basis of the two copies of the Rdeformed Heisenberg algebra. For the finitedimensional representations of the algebra they give a universal description of the states with integer and halfinteger helicity. The infinitedimensional representations correspond formally to the massless states with fractional (real) helicity. The solutions of the latter type, however, break down the (3+1)D Poincaré invariance to the (2+1)D Poincaré invariance, and via a compactification on a circle a consistent theory for massive anyons in d=2+1 is produced. A general analysis of the "helicity equation" shows that the (3+1)D Poincaré group has no massless irreducible representations with the trivial noncompact part of the little group constructed on the basis of the infinitedimensional representations of sl(2, C) . This result is in contrast with the massive case where integer and halfinteger spin states can be described on the basis of such representations, and means, in particular, that the (3+1)D Dirac positive energy covariant equations have no massless limit.
 Publication:

Nuclear Physics B
 Pub Date:
 November 2001
 DOI:
 10.1016/S05503213(01)004424
 arXiv:
 arXiv:hepth/0101190
 Bibcode:
 2001NuPhB.616..419K
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter;
 High Energy Physics  Phenomenology;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 19 pages