Abstract
We describe a five-dimensional analogue of Wigner's operator equation Wa=λPa, where Wa is the Pauli-Lubanski vector, Pa the energy-momentum operator, and λ the helicity of a massless particle. Higher dimensional generalisations are also given.
Highlights
The unitary representations of the Poincare group in four dimensions were classified by Wigner in 1939 [1], see [2] for a recent review
Significant interest in the topic remains due to some unexplored generalisations. It suffices to mention the recent work by Weinberg [6] in which free massless field equations were derived as an incidental consequence of the condition that the invariant Abelian subgroup of the little group is represented trivially on states of a single massless particle
We analyse covariant operator equations that correspond to the irreducible massless representations of ISO0(d − 1, 1) with a finite spin
Summary
The unitary representations of the Poincare group in four dimensions were classified by Wigner in 1939 [1], see [2] for a recent review. Unitary representations of the Poincare group ISO0(d − 1, 1) in higher dimensions, d > 4, have been studied in the literature, see [3,4,5] and references therein. Significant interest in the topic remains due to some unexplored generalisations (including the supersymmetric case) It suffices to mention the recent work by Weinberg [6] in which free massless field equations were derived as an incidental consequence of the condition that the invariant Abelian subgroup of the little group is represented trivially on states of a single massless particle. We analyse covariant operator equations that correspond to the irreducible massless representations of ISO0(d − 1, 1) with a finite (discrete) spin.
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