Solution of the Dirac equation with an axial vector current in the chiral \(\text{SU}(2)\otimes \text{SU}\) model (Q2774328)

The author of this interesting paper considers a standard chiral \(\text{SU}(2)\otimes \text{SU}(2)\) model looking for its ground state at finite density and in connection with this, studies the existence of a self-consistent solution of the Dirac equation in the presence of a source consisting of an axial vector current. The eigenvalue equation for a Dirac nucleon with a spatial axial vector current in the chiral model in a relativistic treatment is solved. The main discussion is concentrated on the correct wave functions of the relativistic nucleon and its implication for the true ground state at finite densities. An approximate expression of the dispersion relation for nucleons together with the mesonic energy is obtained. It is found that the nucleons obey the Dautry-Nyman dispersion relation and are strongly polarized when the \(\sigma \) and \(\pi^{0}\) form a standing wave with non-vanishing axial current. A criterion for AWC, which is applicable to a wide class of chiral \(\text{SU}(2)\otimes \text{SU}(2)\) models is presented. A neutron star whose core is in the AWC phase is expected to have a dipole magnetic field of order \(10^{15-16}\)G.