Relational path integral, effective actions and quantum frame covariance in gravity

• URL: http://arxiv.org/abs/2607.21463v2
• Date: Fri, 24 Jul 2026 13:02:13 GMT
• Title: Relational path integral, effective actions and quantum frame covariance in gravity
• Abstract summary: We propose a relational bundle-geometric formulation of the gravitational path integral by invoking the new tool of quantum reference frames (QRFs)<n>Formulated in terms of correlat (frame-dressed) observables, this yields a manifestly gauge-invariant path integral without ghosts and anomalies.<n>It is equivalent to Faddeev-Popov versions in which the QRF is gauge-fixed, recovering certain previous proposals.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a relational bundle-geometric formulation of the gravitational path integral by invoking the new tool of quantum reference frames (QRFs), which in gravity are gauge-covariant coordinate systems constructed from the available field content. Formulated in terms of relational (frame-dressed) observables, this yields a manifestly gauge-invariant path integral without ghosts and anomalies, and in which observables and their correlators are local to a frame. While eliminating the need for gauge fixing, it is equivalent to Faddeev-Popov versions in which the QRF is gauge-fixed, recovering certain previous proposals. A key feature is its covariance under QRF changes: it is a perspective-neutral path integral which encodes all internal QRF perspectives and the transformations between them. This leads to several qualitative predictions: local correlators and time evolution of relational observables in one QRF perspective become fuzzy in another, and a new spectrum of relational vacua arises. Comprised of frame-dependent no-boundary and asymptotic ground states, a vacuum from one perspective appears generally excited in another. Finally, we construct gauge-invariant, yet frame-dependent effective actions by coupling sources exclusively to relational observables, setting the stage for a relational definition of renormalization.

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