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Manifestly covariant formulation of discrete-spin and real-mass unitary representations of the Poincare group

Marek Czachor
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Abstract

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 $ω_A(p)$.

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Marek Czachor. 1997-01-26. Manifestly covariant formulation of discrete-spin and real-mass unitary representations of the Poincare group. https://arxiv.org/abs/hep-th/9701135

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