The on-shell effective field theory and the chiral anomaly

A new effective field theory has been proposed which describes physical phenomena dominated by on-shell degrees of freedom. It has been recently applied to study the high temperature limit of the photon polarisation tensor of QED for soft external momenta, as it is known that it is dominated by the contribution of the on-shell fermions and antifermions of the plasma. It is possible to generalise the on-shell effective field theory for a non-vanishing value of a chemical potential and chiral chemical potential, and check that also these techniques allow one to study a set of variety of phenomena in these cases. In particular, we will concentrate in the study of chiral anomalous effects at finite density. The student is supposed to learn the basics of the real time formalism of thermal field theory, which generalises QFT from the vacuum to a thermal state, and be able to carry out one-loop calculations with it.