Wigner-Eckart theorem in cosmology: Bispectra for total-angular-momentum waves

Liang Dai, Donghui Jeong, Marc Kamionkowski

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Total-angular-momentum (TAM) waves provide a set of basis functions for scalar, vector, and tensor fields that can be used in place of plane waves and that reflect the rotational symmetry of the spherical sky. Here we discuss three-point correlation functions, or bispectra in harmonic space, for scalar, vector, and tensor fields in terms of TAM waves. The Wigner-Eckart theorem dictates that the expectation value, assuming statistical isotropy, of the product of three TAM waves is the product of a Clebsch-Gordan coefficient (or Wigner-3j symbol) times a function only of the total-angular-momentum quantum numbers. Here we show how this works, and we provide explicit expressions relating the bispectra for TAM waves in terms of the more commonly used Fourier-space bispectra. This formalism will be useful to simplify calculations of projections of three-dimensional bispectra onto the spherical sky.

Original languageEnglish (US)
Article number043504
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number4
StatePublished - Feb 5 2013

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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