Vector-boson condensates, spin-triplet superfluidity of paired neutral and charged fermions, and $3P_2$ pairing of nucleons

Abstract

After reminding of properties of the condensate of the complex scalar field in the external uniform magnetic field $H$ focus is made on the study of phases of the complex neutral vector boson fields coupled with magnetic field by the Zeeman coupling and phases of the charged vector boson fields. These systems may behave as nonmagnetic and ferromagnetic superfluids and ordinary and ferromagnetic superconductors. Response of the ferromagnetic superfluid and superconducting systems occupying half of space on the external uniform static magnetic field $H$ is thoroughly studied. Then the spin-triplet pairing of neutral fermions at conserved spin is considered. Novel phases are found. In external magnetic field the phase with zero mean spin proves to be unstable to the formation of a phase with a non-zero spin. For $H>H_{\rm cr 2}$ the spin-triplet pairing and ferromagnetic superfluidity continue to exist above the "old" phase transition critical temperature $T_{\rm cr}$. For a certain parameter choice ferromagnetic superfluid phases are formed already for $H=0$, characterized by an own magnetic field $h$. Formation of domains is discussed. Next, spin-triplet pairing of charged fermions is studied. Novel phases are found with a ferromagnetic superconductivity. Then, the 3P$_2$ $nn$ pairing in neutron star matter is studied. Also a 3P$_2$ $pp$ pairing is considered. Numerical estimates are performed in the BCS weak coupling limit and beyond it for the $3P_2$ $nn$ and $pp$ pairings, as well as for the 3S$_1$ $np$ pairing.