SPONTANEOUS SYMMETRY BREAKING AND RESPONSE FUNCTIONS IN NEUTRON MATTER

We study the spin response function of an infinite homogeneous system of neutrons interacting through a simple spin-spin Heisenberg force in a non-relativistic context. For a ferromagnetic interaction the spin response along the direction of the spontaneous magnetization displays, for not too large momentum transfers, two distinct peaks. The response along the direction orthogonal to the spontaneous magnetization displays a collective mode to be identified with a Goldstone boson of type II. It is shown that the Goldstone boson contributes to the saturation of the energy-weighted sum rule for ≈ 25% when the system becomes fully magnetized.