Unstable particles in finite volume: The broken phase of the 4-d O(4) non-linear σ-model

Abstract According to a proposal of Luscher 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 σ-model in a Monte-Carlo study on finite lattices. This non-perturbative approach also permits the study of unstable particles, the σ-particle in our case. We observe the σ-resonance and extract its mass and its width.