Heat Trace Asymptotics on Noncommutative Spaces - Vassilevich, D.V. (Symmetry, Integrability and Geometry: Methods and Applications, 2007)
This is a mini-review of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.