  We investigate the vibrational properties of topologically disordered
materials by analytically studying particles that harmonically oscillate around
random positions. Exploiting classical field theory in the thermodynamic limit
at $T=0$, we build up a self-consistent model by analyzing the Hessian
utilizing Euclidean Random Matrix theory. In accordance with earlier findings
[T. S. Grigera et al.J.~Stat.~Mech.~11 (2011) P02015.], we take non-planar
diagrams into account to correctly address multiple local scattering events. By
doing so, we end up with a first principles theory that can predict the main
anomalies of athermal disordered materials, including the boson peak, sound
softening, and Rayleigh damping of sound. In the vibrational density of states,
the sound modes lead to Debye's law for small frequencies. Additionally, an
excess appears in the density of states starting as $\omega^4$ in the low
frequency limit, which is attributed to (quasi-) localized modes.
