Anomalies and Kinetic Theory

Abstract

In this chapter, we will make an overview of the quantum anomalies, as quantities that are no longer conserved when passing from the classical to the quantum realm. We will focus on the chiral anomaly. The discussion will be made in terms of the semiclassical kinetic theory, where the classical Boltzmann transport equation is supplemented by the equations of motion that explicitly contain the Berry connection. In this regard, we will make explicit the connection between the chiral anomaly and the non-trivial topological structure of Weyl semimetals. We will make the discussion beyond the different relaxation time approaches that are commonly used in the literature. This approach introduces some mathematical complexities but also reveals some less known features of transport in Weyl semimetals. Finally, we will discuss other quantum anomalies that have been of interest recently in Condensed Matter Physics.