One-loop corrections to the spectral action

A bstract We analyze the perturbative quantization of spectral action in noncommutative geometry and establish its one-loop renormalizability a generalized sense, while staying within framework geometry. Our result is based on expansion terms higher Yang-Mills Chern-Simons forms. In spirit random geometries, we consider path integral over matrix fluctuations around fixed gauge background show that corresponding counterterms are same form so they can be safely subtracted from action. crucial role will played by appropriate Ward identities, allowing for fully formulation quantum theory at one loop.