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arXiv · 2303.18111

Dynamically implementing the $\overline{\mu}$-scheme in cosmological and spherically symmetric models in an extended phase space model

Kristina Giesel·Hongguang Liu
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Abstract

We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given $\overline{\mu}$-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 Kucha\v{r} decomposition of the extended phase space. The resulting model can be understood as a gauge-unfixed model of a given $\overline{\mu}$-scheme. We use this formalism to investigate the restrictions to the allowed $\overline{\mu}$-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 $\overline{\mu}$-scheme in a top-down derivation from full LQG to symmetry reduced effective models, where for some models only the $\mu_0$-scheme has been obtained so far.

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Kristina Giesel, Hongguang Liu. 2023-03-31. Dynamically implementing the $\overline{\mu}$-scheme in cosmological and spherically symmetric models in an extended phase space model. https://doi.org/10.3390/universe9040176

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