Neutron Star Equation of State and the Possibility of Complex Self-Energy in Landau Theory of Fermi Liquid in Presence of Strong Quantizing Magnetic Field

Using a relativistic version of Landau theory of Fermi liquid with $\sigma-\omega$ and $\rho$ mesons exchange, we have obtained an equation of state for dense neutron star matter in presence of strong quantizing magnetic field. It is found that in this scenario the self energies of both neutron and proton components of dense neutron star matter become complex under certain physical conditions. To be more specific, it is observed that in the exchange diagrams of $\sigma$, $\omega$ and neutral $\rho$ transfer processes and in the direct interaction diagram with $\rho_\pm$ transfer reactions, the nucleon self-energies become complex in nature.