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

TL;DR

This paper presents a covariant formulation for discrete-spin, real-mass unitary representations of the Poincaré group, using a novel p-dependent timelike, spacelike, or null vector t to define eigenstates and Bargmann-Wigner spinors, applicable to both massive and massless cases.

Contribution

It introduces a manifestly covariant approach that avoids Wigner-Mackey induction, utilizing p-dependent vectors to define eigenstates and spinors for Poincaré group representations.

Findings

Provides a covariant eigenvalue problem solution for the Pauli-Lubanski vector.

Constructs Bargmann-Wigner spinors without Wigner-Mackey induction.

Applicable to both massive and massless, on- and off-shell cases.

Abstract

Manifestly covariant formulation of discrete-spin, real-mass unitary representations of the Poincar\'e 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 ($\omega$-spinors) associated with flag pole directions of the spin-frame field $\omega_A(p)$.