# Selberg trace formula The Selberg trace formula was discovered by the Norwegian mathematician Atle Selberg in the 1950s. It provides a deep connection between the geometry of Riemann surfaces and the spectra of differential operators (such as the Laplacian) defined on them. For interacting field theories, we have a generalisation called the Gutzwiller trace formula. In systems exhibiting geodesic motion on hyperbolic surfaces, the Gutzwiller trace formula agrees with the Selberg trace formula. ## Refs - original - [[1957#Selberg]] - interacting fields - [[1970#Gutzwiller]] - [[1971#Gutzwiller]] - see also a book by Gutzwiller: Chaos in Classical and Quantum Mechanics, Chapter 17