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

Recent progresses on QCD phases in a strong magnetic field -- views from Nambu--Jona-Lasinio model

“…The plots are from Ref. [132]. chiral rotation effect, we found a critical electric field eE c = (86.4 MeV) 2 for two-flavor NJL model, below which MCE dominates while above which chiral rotation effect dominates.…”

“…Recalling the explicit form of I c 2 , such validity condition for the ChPT is well satisfied. (4) As well-known, for eE ≫ m 2 π , the QCD vacuum will be unstable against the Schwinger pair production of π + π − or q q, and the feedback should be properly taken into account through the real-time formalism [125,132]. (5) In the chiral limit, (e Īc…”

“…Firstly, we consider the simple case eE = eB = e Ī2 and compare the results of in-out and in-in schemes in Fig. 15 [132]. With π 0 condensate increasing with small…”

“…As we can see, the difference is invisible up to the end of chiral rotation Īc 2 , but the feedback of Schwinger pair production in in-in scheme alters the second-order chiral restoration in in-out scheme to a first-order one at s smaller e Ī2 . Actually, the study of the collective modes indicates that the presumed ground state might be unstable beyond the critical point Īc 2 [132]. If we look at the θ dependence of the thermodynamic potential in Fig.…”

Chirality Production with Mass Effects-Schwinger Pair Production and the Axial Ward Identity

“…9. In contrast to magnetic catalysis, we see that with the addition of an electric field the chiral condensate is weakened, [210][211][212] which acts as an inverse magnetic catalysis effect. One may understand this process intuitively: While a magnetic field would act to strengthen the condensate through spin alignment, an electric field would act to pull the condensate apart, in effect weakening it.…”