All-Plus QED Wavefunctions in de Sitter Space

Abstract

We present a compact all-multiplicity formula for tree-level late-time wavefunction coefficients of scalar QED in four-dimensional de Sitter space, with a conformally coupled charged scalar pair and positive-helicity photons. The result admits both a recursive representation in terms of shifted lower-point coefficients and an explicit finite sum involving only kinematic factors. The flat-space amplitudes vanish for two or more photons, yet the de Sitter coefficients remain nonzero. These zeros enforce cancellations of the total-energy residue and, through factorization, of proper partial-energy residues involving multi-photon subamplitudes. Using a common-reference construction, we derive an exact lower-point recursion from Abelian Ward identities. Conformal symmetry provides an independent check: the partition sum solves the inhomogeneous Ward identity, while the total-energy term is a homogeneous solution. We also outline an analogous recursion in massless fermionic QED.

5 pages, v2: A non-recursive representation for the all-multiplicity formula added