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Celestial decomposition of Wigner’s particles

Lorenzo Iacobacci* and Kevin Nguyen†

  • *Contact author: lorenzoiacobacci@gmail.com
  • †Contact author: kevin.nguyen2@ulb.be
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Phys. Rev. D 111, 125010 – Published 16 June, 2025

DOI: https://doi.org/10.1103/snfw-gbbc

Abstract

We provide a detailed decomposition of Wigner’s particles, defined as unitary irreducible representations of the Poincaré group, in terms of unitary representations of its Lorentz subgroup. As pointed out before us, this decomposition only involves Lorentz representations belonging to the principal continuous series, and further underpins the connection between scattering amplitudes and conformal correlation functions discussed in the context of celestial holography. We provide very explicit formulas for the decomposition of particles of arbitrary mass and (half-)integer spin and for any spacetime dimension. We emphasize that this decomposition is unique and comes equipped with a specific inner product on the corresponding Hilbert space. We also confirm that unitary translations mix Lorentz representations within the principal continuous series only, as required. Implications to the celestial holography program are indicated.

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Phys. Rev. D 111, 125010– Published 16 June, 2025
  • Received 4 April 2025
  • Accepted 28 May 2025
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