Electrons interacting with Goldstone modes and the rotating frame

We consider electronic systems with a spontaneously broken continuous symmetry. The scattering vertex between electrons and Goldstone modes is calculated over the entire Brillouin zone using the random phase approximation. This calculation reveals two things: (1) electrons always couple to both 0 and partial differential t0, where 0 is the Goldstone field, and (2) quasiparticles in a state with continuous symmetry breaking have to be defined in a rotating frame, which locally follows the fluctuations of the order parameter. The implications of these findings for electron spectral functions in both symmetry -broken and thermally disordered systems are discussed, and the examples of antiferromagnetism in the Hubbard model and spin spiral order in the three -band model are worked out in detail.