A Kucha\v{r} Hypertime Formalism For Cylindrically Symmetric Spacetimes With Interacting Scalar Fields

The Kucha\v{r} canonical transformation for vacuum geometrodynamics in the presence of cylindrical symmetry is applied to a general non-vacuum case. The resulting constraints are highly non-linear and non-local in the momenta conjugate to the Kucha\v{r} embedding variables. However, it is demonstrated that the constraints can be solved for these momenta and thus the dynamics of cylindrically symmetric models can be cast in a form suitable for the construction of a hypertime functional Schr"odinger equation.