Unstable particles in finite volume: The broken phase of the $4$-d   $O(4)$ non-linear $\sigma$-model
  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. 
Frank Zimmermann, J\"org Westphalen, Meinulf G\"ockeler and Hans A.   Kastrup