Dynamically implementing the μ-bar-scheme in cosmological and spherically symmetric models in an extended phase space model - Giesel, Kristina; Liu, Hongguang (Universe, 2023)
We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given μ¯" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">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¯" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">μ¯¯-scheme. We use this formalism to investigate the restrictions to the allowed μ¯" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">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¯" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">μ¯¯-scheme in a top-down derivation from full LQG to symmetry-reduced effective models, where, for some models, only the μ0" role="presentation" style="max-height: none; display: inline; line-height: normal; font-size: 13.2px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; caret-color: rgb(34, 34, 34); color: rgb(34, 34, 34); font-family: Arial, Arial, Helvetica, sans-serif; position: relative;">μ0-scheme has been obtained thus far.<br