The electromagnetic field effects in in-out and in-in formalisms

Abstract

In this work, we compare the effects of electromagnetic (EM) fields on strong coupling systems in two formalisms: in-out and in-in, which are different from each other when a finite electric field is present. The chiral effective Nambu–Jona-Lasinio model is adopted for this study, and two kinds of EM field distributions are considered: pure electric field and parallel EM (PEM) field with equal electric and magnetic components. For both distributions, we find that the results of in-out and in-in formalisms start to diverge when the electric field (qE)1/2 is larger than the chiral effective mass M=[m2+(π0)2]1/2, that is, when the Schwinger pair production mechanism becomes important. Besides, the chiral restorations are stiffer in the in-in formalism, especially the transition shifts to first-order instead of the second-order for the PEM field. The neutral collective modes are also explored accordingly: For the PEM field, more precise calculations show nonmonotonic features of their pole masses due to parity mixing, and then the Goldstone-like mode is found to be noneffective at the end of chiral rotation because of chiral anomaly.