Conformal basis for flat space amplitudes

May 2, 2017
17 pages
Published in:
  • Phys.Rev.D 96 (2017) 6, 065022
  • Published: Sep 25, 2017
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Abstract: (APS)
We study solutions of the Klein-Gordon, Maxwell, and linearized Einstein equations in R1,d+1 that transform as d-dimensional conformal primaries under the Lorentz group SO(1,d+1). Such solutions, called conformal primary wavefunctions, are labeled by a conformal dimension Δ and a point in Rd, rather than an on-shell (d+2)-dimensional momentum. We show that the continuum of scalar conformal primary wavefunctions on the principal continuous series Δ∈d2+iR of SO(1,d+1) spans a complete set of normalizable solutions to the wave equation. In the massless case, with or without spin, the transition from momentum space to conformal primary wavefunctions is implemented by a Mellin transform. As a consequence of this construction, scattering amplitudes in this basis transform covariantly under SO(1,d+1) as d-dimensional conformal correlators.
Note:
  • 37 pages, 4 tables
  • dimension: conformal
  • Einstein equation: linear
  • group: Lorentz
  • scattering amplitude
  • correlation function
  • spin