LAUSR

We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given μ¯-scheme can be implemented dynamically. These models are constructed in the context of the relational formalism by using a canonical transformation on the extended phase space, which provides a Kuchař decomposition of the extended phase space. The resulting model can be understood as a gauge-unfixed model of a given μ¯-scheme. We use this formalism to investigate the restrictions to the allowed μ¯-scheme from this perspective and discuss the differences in the cosmological and spherically symmetric case. This method can be useful, for example, to obtain a μ¯-scheme in a top-down derivation from full LQG to symmetry-reduced effective models, where, for some models, only the μ0-scheme has been obtained thus far.