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.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Universiteit Utrecht / University of Utrecht [UU]
- 2 Uppsala universitet / Uppsala University
- 3 Universidade Federal do Rio de Janeiro / Federal University of Rio de Janeiro [UFRJ]
- 4 Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN]
- 5 Stockholm University [Univ Stockholm]
- Conselho Nacional de Desenvolvimento Científico e Tecnológico / National Council for Scientific and Technological Development [CNPq]
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (through Organization: Coordenação de Aperfeicoamento de Pessoal de Nível Superior [CAPES])
- Knut och Alice Wallenbergs Stiftelse (Knut and Alice Wallenberg Foundation) (through Organization: Knut och Alice Wallenbergs Stiftelse / Knut and Alice Wallenberg Foundation)
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek / Netherlands Organisation for Scientific Research [NWO]