2017/05/11 by Bruno Mera, Mera, B.
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum and electron transport phenomena #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.1705.04394
openalex publication_date 2017/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a detailed path integral derivation of the topological response of gapped free fermions, in 2+1 dimensions, to an external U(1) Gauge field. The well-known Hall response is obtained by identifying the Chern-Simons term in the effective action with the correct coefficient. We extend the result to 2d+1 dimensions in which the response is associated to a Chern-Simons term with a coefficient related to a characteristic class coming from topological band theory. We comment on the bulk-to-boundary principle which arises naturally when one considers the theory on a manifold with boundary.