Possible Origin of Magnetic Fields in Very Dense Stars

We discuss the bosonization of a relativistic very dense Fermi gas in a magnetic field and the consequent Bose--Einstein condensation of the resulting relativistic vector gas of charged particles. The model may be applied to paired spin-up electrons. We show that such systems may maintain self-consistently magnetic fields of order 10¹⁰-10¹³ G. That pairing could be the origin of large magnetic fields in some white dwarfs and neutron stars. For fields large enough (～ 10¹³ for white dwarfs), the system becomes unstable and collapses.