Anomaly mechanism at finite temperature

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Abstract
The chirality-breaking effects associated with the axial anomaly at finite temperature are studied. The exact results are obtained in the case when the interaction between fermions in a heat bath is neglected. When the temperature is much greater than the characteristic frequencies and momenta of external fields, the dominant contribution to the anomaly is due not to the pair-creation processes associated with the level-crossing mechanism but rather to the scattering of the existing thermal fermion excitations by the external fields. In two-dimensional QED analyzed in particular detail, this scattering results in an overall shift of momenta of the electrons and positrons in the heat bath. This shift brings about a change of the total chirality required by the anomaly. To account for nontrivial interaction effects is difficult technically. We suggest, however, a simple nonlocal field-theory model imitating some distinguishing features of a quark-gluon plasma. It turns out that nonlocality leads to the appearance of massless ghost states which play a crucial role in saturating the chiral anomaly. The implications of this analysis for the quark-gluon plasma, the physical system of interest, are discussed in detail.