Gravity-matter mini-superspace: quantum regime, classical regime and in between

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Abstract
Within a mini-superspace model for gravity coupled to matter, the authors review how the Wheeler-DeWitt equation can be rearranged to resemble semiclassical equations of motion for gravity interacting with matter. They extend this approach to arrive at a fully classical description. They construct approximate solutions of the semiclassical equations and discuss in some detail the various correction terms that emerge in the transition from a quantum to a classical description.