Heat Trace Asymptotics on Noncommutative Spaces

TL;DR

This paper reviews the heat kernel expansion for generalized Laplacians on noncommutative spaces, discussing its applications to spectral actions, renormalization, and anomalies in noncommutative geometry.

Contribution

It provides a concise overview of heat trace asymptotics in noncommutative spaces and explores their implications in spectral action and quantum field theory.

Findings

Heat kernel expansion techniques are applicable to noncommutative geometries.

Applications to spectral action principles are discussed.

Implications for renormalization and anomalies are considered.

Abstract

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.