Chiral Anomaly, Dirac Sea and Berry monopole in Wigner Function Approach

Abstract

Within Wigner function formalism, the chiral anomaly arises naturally from the Dirac sea contribution in un-normal-ordered Wigner function. For massless fermions, the Dirac sea contribution behaves like a 4-dimensional or 3-dimensional Berry monopole in Euclidian momentum space, while for massive fermions, although Dirac sea still leads to the chiral anomaly but there is no Berry monopole at infrared momentum region. We discuss these points explicitly in a simple and concrete example.

Comments: 5 pages, Contribution to the proceedings of XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2019)