Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-01-27
Nucl.Phys.B616:419-436,2001
Physics
High Energy Physics
High Energy Physics - Theory
19 pages; minor changes, references added. To appear in Nucl. Phys. B
Scientific paper
10.1016/S0550-3213(01)00442-4
We construct the covariant, spinor sets of relativistic wave equations for a massless field on the basis of the two copies of the R-deformed Heisenberg algebra. For the finite-dimensional representations of the algebra they give a universal description of the states with integer and half-integer helicity. The infinite-dimensional representations correspond formally to the massless states with fractional (real) helicity. The solutions of the latter type, however, break down the (3+1)$D$ Poincar\'e invariance to the (2+1)$D$ Poincar\'e 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)$D$ Poincar\'e group has no massless irreducible representations with the trivial non-compact part of the little group constructed on the basis of the infinite-dimensional representations of $sl(2,\CC)$. This result is in contrast with the massive case where integer and half-integer 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.
de Traubenberg Michel Rausch
Klishevich Sergey M.
Plyushchay Mikhail S.
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