The Weyl Anomaly and the Nature of the Background Geometry (original) (raw)

The paper examines the implications of using Riemann versus Weyl geometries in the framework of general relativity, asserting that Riemann geometry may be inadequate due to its non-conformally invariant nature. The authors discuss the interaction between background geometry and the dynamics of matter fields, highlighting the occurrence of the Weyl anomaly and suggesting that a transition to a Weyl-based geometric framework might resolve this anomaly. The findings indicate a potential reevaluation of the foundations of gravitational theories, advocating for a more fundamental understanding of geometry in the context of quantum fields.