Relativistic partial waves for celestial amplitudes

Abstract

The formalism of relativistic partial wave expansion is developed for four-point celestial amplitudes of massless external particles. In particular, relativistic partial waves are found as eigenfunctions to the product representation of celestial Poincaré Casimir operators with appropriate eigenvalues. The requirement of hermiticity of Casimir operators is used to fix the corresponding integral inner product, and orthogonality of the obtained relativistic partial waves is verified explicitly. The completeness relation, as well as the relativistic partial wave expansion follow. Example celestial amplitudes of scalars, gluons, gravitons and open superstring gluons are expanded on the basis of relativistic partial waves for demonstration. A connection with the formulation of relativistic partial waves in the bulk of Minkowski space is made in appendices.

arXiv comment26 pages, no figures, published version

References in corpus (32)

• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• A holographic reduction of Minkowski space-time
• Gluon Amplitudes as 2d Conformal Correlators
• Conformally Soft Photons and Gravitons
• Conformally Soft Theorem in Gauge Theory
• Celestial amplitudes and conformal soft theorems
• Asymptotic Symmetries and Celestial CFT
• Symmetries of Celestial Amplitudes
• Conformally Soft Theorem In Gravity
• Null Infinity and Unitary Representation of The Poincare Group
• Strings on Celestial Sphere
• Tree-level gluon amplitudes on the celestial sphere
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• Extended BMS Algebra of Celestial CFT
• BMS Symmetry of Celestial OPE
• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• Extended Super BMS Algebra of Celestial CFT
• Double Copy for Celestial Amplitudes
• Uplifting AdS3/CFT2 to Flat Space Holography
• Primary Fields in Celestial CFT
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Conformal Structure of Massless Scalar Amplitudes Beyond Tree level
• Modified celestial amplitude in Einstein gravity
• Celestial Current Algebra from Low's Subleading Soft Theorem
• Conformal properties of soft-operators - 1 : Use of null-states
• Symmetries of free massless particles and soft theorems
• On loop celestial amplitudes for gauge theory and gravity
• On Sugawara construction on Celestial Sphere
• Massive Spinning Bosons on the Celestial Sphere
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering

Cited by in corpus (21)

• Lectures on Celestial Amplitudes
• Shifting Spin on the Celestial Sphere
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Conformal Blocks from Celestial Gluon Amplitudes
• Lectures on Celestial Holography
• Loops on the Celestial Sphere
• Conformal Primary Basis for Dirac Spinors
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• Descendants in celestial CFT and emergent multi-collinear factorization
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Bulk locality from the celestial amplitude
• Conformally Soft Fermions
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Celestial amplitudes in an ambidextrous basis
• Celestial IR divergences and the effective action of supertranslation modes
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• Celestial OPE blocks
• Celestial Holography
• $sl(2,\mathds{C})\times D$ symmetry and conformal primary basis for massless fields
• Celestial Regge theory