@article{oai:oist.repo.nii.ac.jp:00002257,
 author = {Höhn, Philipp A. and Smith, Alexander R. H. and Lock, Maximilian P. E.},
 issue = {587083},
 journal = {Frontiers in Physics},
 month = {Jun},
 note = {We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks.},
 title = {Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings},
 volume = {9},
 year = {2021}
}