A note on the representations of SO(1,d + 1)

2024/06/05 by Zimo Sun · 35 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebra over a field #Mathematical physics #Mathematics #Physics #Pure mathematics #Theoretical physics

paper · doi:10.1142/s0129055x24300073

published in Reviews in Mathematical Physics 37(01) (World Scientific)

openalex publication_date 2024/06/05 · openalex created_date 2024/06/06 · openalex updated_date 2026/08/04

Abstract

[Formula: see text] is the isometry group of [Formula: see text]-dimensional de Sitter spacetime ([Formula: see text]) and the conformal group of [Formula: see text]. This note gives a pedagogical introduction to the representation theory of [Formula: see text], from the perspective of de Sitter quantum field theory and using tools from conformal field theory. Topics include (1) the construction and classification of all unitary irreducible representations (UIRs) of [Formula: see text] and [Formula: see text], (2) the construction and classification of all UIRs of [Formula: see text] that describe integer-spin fields in [Formula: see text], (3) a physical framework for understanding these UIRs, (4) the definition and derivation of Harish-Chandra group characters of [Formula: see text] and (5) a comparison between UIRs of [Formula: see text] and [Formula: see text].

Citations

• Irreducible Unitary Representations of the Lorentz Group
• On Unitary Representations of the Group of De Sitter Space
• Light-ray operators in conformal field theory

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