  We define equivariant open Gromov-Witten invariants for
$\mathbb{R}\mathbb{P}^{2m} \hookrightarrow \mathbb{C}\mathbb{P}^{2m}$ as sums
of integrals of equivariant forms over resolution spaces, which are blowups of
products of moduli spaces of stable disc-maps modeled on trees. These
invariants encode the quantum deformation of the equivariant cohomology of
$\mathbb{R}\mathbb{P}^{2m}$ by holomorphic discs in $\mathbb{C}\mathbb{P}^{2m}$
and, for $m=1$, specialize to give Welschinger's signed count of real rational
planar curves in the non-equivariant limit.
