Area discreteness, Lorentz covariance and Hilbert space non-separability

TL;DR

This paper demonstrates that quantum area discreteness aligns with Lorentz covariance in a loop quantum gravity framework, with Hilbert space non-separability playing a key role, potentially relating to observer perspectives.

Contribution

It shows how area quantization is compatible with Lorentz boosts in a diffeomorphism-invariant quantum field theory, highlighting the role of Hilbert space non-separability.

Findings

Quantum area discreteness is consistent with Lorentz covariance.

Hilbert space non-separability is crucial for this consistency.

Observer perspectives may be linked to Hilbert space non-separability.

Abstract

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.