Conformal basis for flat space amplitudes
May 2, 201717 pages
Published in:
- Phys.Rev.D 96 (2017) 6, 065022
- Published: Sep 25, 2017
e-Print:
- 1705.01027 [hep-th]
View in:
Citations per year
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
References(57)
Figures(0)
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