1997/01/26 by Marek Czachor
Physics and Astronomy · #hep-th #quant-ph
published as published with minor extensions as "Bargmann-Wigner spinors", Photon and Poincare Group, ed. V.V.Dvoeglazov, pp. 32-62 (Nova, NY, 1999) · revtex, 21 pages, submitted to Proc.Roy.Soc.London
arxiv created 1997/01/26 · arxiv updated 2009/11/30
Manifestly covariant formulation of discrete-spin, real-mass unitary representations of the Poincaré group is given. We begin with a field of spin-frames associated with 4-mometa p and use them to simplify the eigenvalue problem for the Pauli-Lubanski vector projection in a direction given by a world-vector t. As opposed to the standard treatments where t is a constant time direction, our t is in general p-dependent and timelike, spacelike or null. The corresponding eigenstates play a role of a basis used to define Bargmann-Wigner spinors which form a carrier space of the unitary representation. The construction does not use the Wigner-Mackey induction procedure, is manifestly covariant and works simultaneously in both massive and massless cases (in on- and off-shell versions). Of particular interest are special Bargmann-Wigner spinors (ω-spinors) associated with flag pole directions of the spin-frame field ωA(p).