Conformal metric fluctuations and quantum mechanics

Critical matter and geometric phase transitions

“…Given the local nature of the interaction between matter and geometry, it seems most natural to expect the metric to respond in kind to matter fluctuations. Other authors have considered fluctuations in general relativity (see, e.g., [20]); however, such work has generally been posed within the context of quantum or semi-classical gravity. In the case of critical phenomena, at least at the level where the microscopic details are irrelevant, it is sufficient to consider the properties of classical fields.…”