Equivalence of approaches to relational quantum dynamics in relativistic settings

Understand

We have previously shown (arXiv:1912.00033) 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.
• We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
• This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum.