Area discreteness, Lorentz covariance and Hilbert space non-separability
General Relativity and Quantum Cosmology
2026-01-06 v1
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.
Cite
@article{arxiv.2601.01198,
title = {Area discreteness, Lorentz covariance and Hilbert space non-separability},
author = {Madhavan Varadarajan},
journal= {arXiv preprint arXiv:2601.01198},
year = {2026}
}
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16 pages