We calculate the leading radiative corrections to the axial current in the chiral separation effect in dense QED in a magnetic field. Contrary to the conventional wisdom, suggesting that the axial current should be exactly fixed by the chiral anomaly relation and is described by the topological contribution on the lowest Landau level in the free theory, we find in fact that the axial current receives nontrivial radiative corrections. The direct calculations performed to the linear order in the external magnetic field show that the nontrivial radiative corrections to the axial current are provided by the Fermi surface singularity in the fermion propagator at nonzero fermion density.

We calculate the electron self-energy in a magnetized QED plasma to the leading perturbative order in the coupling constant and to the linear order in an external magnetic field. We find that the chiral asymmetry of the normal ground state of the system is characterized by two new Dirac structures. One of them is the familiar chiral shift previously discussed in the Nambu-Jona-Lasinio model. The other structure is new. It formally looks like that of the chiral chemical potential, but is an odd function of the longitudinal component of the momentum, directed along the magnetic field. The origin of this new parity-even chiral structure is directly connected with the long-range character of the QED interaction. The form of the Fermi surface in the weak magnetic field is determined.

We investigate both (pseudo)scalar mesons and diquarks in the presence of external magnetic field in the framework of the two-flavored Nambu-Jona-Lasinio (NJL) model, where mesons and diquarks are constructed by infinite sum of quark-loop chains by using random phase approximation. The polarization function of the quark-loop is calculated to the leading order of 1/Nc expansion by taking the quark propagator in the Landau level representation. We systematically investigate the masses behaviors of scalar σ meson, neutral and charged pions as well as the scalar diquarks, with respect to the magnetic field strength at finite temperature and chemical potential. It is shown that the numerical results of both neutral and charged pions are consistent with the lattice QCD simulations. The mass of the charge neutral pion keeps almost a constant under the magnetic field, which is preserved by the remnant symmetry of QCD×QED in the vacuum. The mass of the charge neutral scalar σ is around two times quark mass and increases with the magnetic field due to the magnetic catalysis effect, which is an typical example showing that the polarized internal quark structure cannot be neglected when we consider the meson properties under magnetic field. For the charged particles, the one quark-antiquark loop contribution to the charged π ± increases essentially with the increase of magnetic fields due to the magnetic catalysis of the polarized quarks. However, the one quark-quark loop contribution to the scalar diquark mass is negative comparing with the point-particle result and the loop effect is small.

We study the chiral phase transition of quark matter under rotation in two-flavor Nambu-Jona-Lasinio (NJL) model. It is found that, in the rotating frame, the angular velocity plays the similar role as the baryon chemical potential and suppresses the chiral condensate, thus the chiral phase transition shows a critical end point not only in the temperature-chemical potential T − µ plane, but also in the temperature-angular momentum T − ω plane. One interesting observation is that in the T − µ plane, the presence of the angular momentum only shifts down the critical temperature T E of the CEP and does not shift the critical chemical potential µ E , and in the T − ω plane, the increase of the chemical potential only shift down the critical temperature T E and does not change the critical angular momentum ω E . The phase structure in the T − µ plane is sensitive to the coupling strength in the vector channel, while the phase structure in T − ω plane is not. It is also observed that the rotating angular velocity suppresses the kurtosis of the baryon number fluctuations, while it enhances the pressure density, energy density, the specific heat and the sound velocity.