Quantum Field Theory Anomalies in Condensed Matter Physics

TL;DR

This paper provides a comprehensive introduction to quantum anomalies and their significance in condensed matter physics, illustrating with examples like topological insulators and Weyl semimetals.

Contribution

It offers a pedagogical overview of quantum anomalies, their calculation methods, and their role in explaining topological phases in condensed matter systems.

Findings

Quantum anomalies are crucial for understanding topological states.

Examples include quantum Hall liquids and Weyl semimetals.

The paper clarifies the calculation and physical implications of anomalies.

Abstract

We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global anomalies. We illustrate the theory with examples such as quantum Hall liquids, Fermi liquids, Weyl semi-metals, topological insulators and topological superconductors. The required background is basic knowledge of quantum field theory, including fermions and gauge fields, and some familiarity with path integral and functional methods. Some knowledge of topological phases of matter is helpful, but not necessary.