Quantum cosmological intertwining: Factor ordering and boundary conditions from hidden symmetries

We explore the implications of hidden symmetries present in a particular quantum cosmological setting, extending the results reported in [1, 2]. In more detail, our case study is constituted by a spatially closed Friedmann-Lemaˆotre-Robertson-Walker universe, in the presence of a conformally coupled scalar field. The su(1,1) hidden symmetries of this model, together with the Hamiltonian constraint, lead to the gauge invariance of its corresponding Bargmann indices. We subsequently show that some factor-ordering choices can be related to the allowed spectrum of Bargmann indices and hence, to the hidden symmetries. Moreover, the presence of those hidden symmetries also implies a set of appropriate boundary conditions to choose from. In summary, our results suggest that factor ordering and boundary conditions can be intertwined when a quantum cosmological model has hidden symmetries.