2024/11/28 by Lorenzo Iacobacci, Iacobacci, Lorenzo, Kevin P. Nguyen +1 · 2 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2411.19219
openalex publication_date 2024/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 formulae for the decomposition of particles of arbitrary mass and (half-)integer spin and for any spacetime dimension. We emphasise that this decomposition is unique and comes 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.