Out-of-equilibrium $U_A\mathbf{(}1\mathbf{)}$ symmetry breaking in electromagnetic fields

We systematically study quantum effect on chiral and $U_A(1)$ symmetry breaking under external electromagnetic fields in the frame of equal-time Wigner function formalism. We derive the transport and constraint equations for the quark distribution functions and the chiral and pion condensates in a Nambu–Jona-Lasinio model. By taking semiclassical expansion of the equations, chiral symmetry is broken at classical level, while $U_A(1)$ symmetry breaking happens only at quantum level. Beyond quasiparticle approximation, the quark off-shell effect leads to strong oscillation for the chiral and pion condensates.

Figure 1

The time evolution of chiral condensate $\sigma (t)$ (dashed line) and pion condensate $\pi (t)$ (solid line).