  According to a proposal of L\"uscher it is possible to determine elastic
scattering phases in infinite volume from the energy spectrum of two-particle
states in a periodic box.
  We demonstrate the applicability of this method in the broken phase of the
4-dimensional $O(4)$ non-linear $\sigma$-model in a Monte-Carlo study on finite
lattices.
  This non-perturbative approach also permits the study of unstable particles,
the $\sg$-particle in our case. We observe the $\sg$-resonance and extract its
mass and its width.
