Area discreteness, Lorentz covariance and Hilbert space non-separability

We show how quantum discreteness of spatial area is consistent with a unitary implementation of Lorentz boosts in an LQG type quantization of a diffeomorphism invariant reformulation of free scalar field theory on 2d flat spacetime known as Parameterized Field Theory (PFT). This consistency is a result of Hilbert space non-separability which is a characteristic feature of LQG representations. Our results suggest a possible interpretation of Hilbert space non-separability in terms of observer perspectives.