A simple construction of Heat Kernels and conformal anomalies via Fedosov deformation quantization

Abstract

We propose a new approach to the systematic computation of the heat-kernel expansion and, in particular, of conformal anomalies, based on Fedosov deformation quantization. The approach is fully covariant, applies to differential operators of arbitrary order, is amenable to efficient implementation, and yields closed-form expressions. As applications, we compute conformal anomalies in four, six, and eight dimensions, the last being a new result.