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arXiv · 2605.22260

The Limitations of the Notion of `Observable' in Diffeomorphism-Invariant Models

Álvaro Mozota Frauca
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Abstract

The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with this symmetry and building quantum versions of them. In this article I distinguish between two senses of gauge transformation: local and global, and I argue that the notion of observable appears more naturally in the local sense of gauge transformation. Then, I argue that diffeomorphism invariance can be understood as a gauge symmetry only from a global point of view, and hence, that the concept of observable applies only in a restricted manner. This has the consequence that some popular claims in the literature, such as the claim that the physical content of diffeomorphism-invariant models is encoded in correlations, are unfounded.

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Álvaro Mozota Frauca. 2026-05-21. The Limitations of the Notion of `Observable' in Diffeomorphism-Invariant Models. https://doi.org/10.1086/741910

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