  We present a microscopic theory of zero-temperature order parameter and
pseudospin stiffness reduction due to quantum fluctuations in the ground state
of double-layer quantum Hall ferromagnets. Collective excitations in this
systems are properly described only when interactions in both direct and
exchange particle-hole channels are included. We employ a functional integral
approach which is able to account for both, and comment on its relation to
diagrammatic perturbation theory. We also discuss its relation to Gaussian
fluctuation approximations based on Hubbard-Stratonovich-transformation
representations of interactions in ferromagnets and superconductors. We derive
remarkably simple analytical expressions for the correlation energy,
renormalized order parameter and renormalized pseudospin stiffness.
