The static and dynamic response associated with a low concentration x of static defects in a Heisenberg antiferromagnet at zero temperature is analyzed within linearized spin-wave theory via a boson formalism involving a non-Hermitian potential. We obtain the dispersion relation for long-wavelength spin waves in the form ω(q)=c(x)q+iγ(x)qτ. Our results for c(x) agree with previous work and, in particular, give c(x)=c(0)[1-αx+O(x2)], where the coefficient α, which can be related to the helicity modulus and the uniform perpendicular susceptibility, diverges in the limit d→2, where d is the spatial dimensionality. One major result is that τ=d-1 for defects whose spin S’ is different from that (S) of the host lattice and τ=d+1 when S’=S. Thus d=2 (which is the case for the copper oxide antiferromagnets) is the lower critical dimension at which infrared divergences affect the dynamic response due to vacancies (S’=0). To elucidate our results we consider the way the antiferromagnetic symmetry is broken when defects occur unequally on the two sublattices, and our results are consistent with previous general hydrodynamic arguments. We give detailed expressions for the actual spin susceptibility in terms of the boson response function. We also consider how defects affect the zero-point contribution to magnetization and density of states.