Magnetic moment of constituent fermions in ground states with spontaneously broken translational invariance

We especially consider the high baryon density π0 condensed phase, in which chiral symmetry is spontaneously broken, with space varying expectation values of the σ and π0 fields. This phase has a spin polarized Fermi sea as the ground state. We show that there is indeed generated a macroscopic magnetization in this phase, contrary to what one would have found, if one just used a primitive phenomenological magnetic moment formula for explicit/current fermion masses. This is important in the context of neutron stars, as such a high density state may be responsible for very high magnetic fields in the dense core of neutron stars.