Out-of-equilibrium chiral and $U_A(1)$ symmetry breaking in electromagnetic fields

Understand

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 semi-classical expansion of the equations, chiral symmetry is broken at classical level, while $U_A(1)$ symmetry breaking happens only at quantum level.
• Beyond quasi-particle approximation, the quark off-shell effect leads to strong oscillation for the chiral and pion condensates.