A groupoidal approach to quantum reference frames

• URL: http://arxiv.org/abs/2608.14133v1
• Date: Fri, 14 Aug 2026 09:39:26 GMT
• Title: A groupoidal approach to quantum reference frames
• Abstract summary: We develop the kinematical and operator-algebraic foundations of a groupoid-based relational quantum field theory.<n>We prove that the groupoid QRF construction reduces to the standard operational QRF formalism for locally compact groups.<n>We show that covariant POVMs are $$-continuous with respect to quasi-invariant $$-finite positive Borel measures.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop the kinematical and operator-algebraic foundations of a groupoid-based relational quantum field theory (RQFT) on curved spacetimes. Indeed, the usual group-based quantum reference frame (QRF) formalism is not directly suited to generic curved Lorentzian backgrounds as global symmetry groups are typically absent or too small. We formulate a notion of QRF for a continuous groupoid. This yields a groupoid relativization map and relational observables. We show that a localization limit recovers the ordinary non-relational description. We construct canonical sharp groupoid QRFs, which form the groupoidal counterpart of the ideal group QRFs based on $L^2(G)$. We further prove that the groupoid QRF construction reduces to the standard operational QRF formalism for locally compact groups. The action groupoid QRFs are torsor QRFs only for specific classes of fields of positive operator-valued measures (POVMs), and the torsor relativization map only applies to constant operator fields of system observables. We review the foundations of RQFT in Minkowski spacetime. We prove new results that further link RQFT to Wightman QFT. We show that covariant POVMs are $μ$-continuous with respect to quasi-invariant $σ$-finite positive Borel measures $μ$. Thus, relational quantum fields can be understood as the smearing of pointwise-defined kernels with respect to the QRF's statistics. We develop RQFT in curved spacetime, where we argue that the correct replacement for the Poincaré group is the Poincaré groupoid of the spacetime. We also indicate how the framework extends further to internal gauge symmetry and relational gauge-covariant quantum field theory via Atiyah groupoids, providing a first step towards formulating a relational quantum Yang-Mills field theory.

Related papers

• Relational path integral, effective actions and quantum frame covariance in gravity [0.0]
  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.
  arXiv  Detail & Related papers  (2026-07-23T16:07:02Z)
• Conceptual and Geometric Foundations for a Teleparallel Approach to Quantum Gravity [45.88028371034407]
  We revisit quantum field theory in curved spacetime as a semi-classical framework for quantum matter on classical geometries.<n>We outline a teleparallel framework based on coframe and spin-connection variables, where gravity is encoded in torsion rather than string curvature.
  arXiv  Detail & Related papers  (2026-06-08T15:02:26Z)
• Anomalous Mixed-State Floquet Topology in One-Dimensional Open Quantum Systems [41.99844472131922]
  We investigate the non-equilibrium topology of a periodically driven, dissipative Su-Schrieffer-Heeger chain.<n>We show that the steady state can be characterised by a Hermitian purity spectrum.<n>We identify a pair of topological invariants $(0_mathrmEGP, _mathrmEGP)$, revealing a structure consistent with a $mathbbZtimesmathbbZ$ classification known from isolated Floquet SSH systems.
  arXiv  Detail & Related papers  (2026-04-28T05:54:40Z)
• Error Correction in Lattice Quantum Electrodynamics with Quantum Reference Frames [1.177047754711803]
  Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against noise.<n>We ask whether gauge theories can be understood in similar terms, and make this idea concrete in lattice quantum electrodynamics.
  arXiv  Detail & Related papers  (2026-04-07T17:51:56Z)
• Exactly Solvable RD Model: RG Cycles Meet Fractality [45.88028371034407]
  We consider the Bethe ansatz integrable Russian Doll (RD) model of superconductivity with time-reversal symmetry breaking.<n>By obtaining an exact solution for the renormalization group flows, we investigate the phase structure in the one-pair sector.<n>We show that the quantum number Q, arising from the Bethe ansatz equations, counts the number of cycles and parametrizes the towers of states.
  arXiv  Detail & Related papers  (2026-03-18T12:54:21Z)
• Shortcuts to adiabaticity, unexciting backgrounds, and reflectionless potentials [45.88028371034407]
  We exploit the analogy with one-dimensional quantum mechanics, and the well known correspondence between Bogoliubov coefficients in the QHO and transmission/reflection amplitudes in scattering theory.<n>We show how STA completions can be understood in terms of the anti-squeezing operator.
  arXiv  Detail & Related papers  (2026-01-16T13:02:37Z)
• Foundations of Relational Quantum Field Theory I: Scalars [0.0]
  We develop foundations for a relational approach to quantum field theory (RQFT) based on the operational quantum reference frames (QRFs) framework considered in a relativistic setting.<n>We focus on scalar fields in Minkowski spacetime and discuss the emergence of relational local (bounded) observables and (pointwise) fields.<n>We show how the properties of algebras generated by relational local observables extend the core axioms of Algebraic QFT.
  arXiv  Detail & Related papers  (2025-07-29T09:01:38Z)
• Relational entanglement entropies and quantum reference frames in gauge theories [0.0]
  We show that defining gravitational entanglement entropies relative to quantum reference frames (QRFs) intrinsically regularizes them.<n>Our work unifies and extends previous approaches and reveals the interplay between entropies and regional symmetry structures.
  arXiv  Detail & Related papers  (2025-06-30T01:43:11Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• A Floquet-Rydberg quantum simulator for confinement in $\mathbb{Z}_2$ gauge theories [44.99833362998488]
  Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators. We present a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a $mathbbZ$ LGT. We show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques.
  arXiv  Detail & Related papers  (2023-11-28T13:01:24Z)
• Perspective-neutral approach to quantum frame covariance for general symmetry groups [0.0]
  Internal quantum reference frames (QRFs) appear widely in the literature on quantum gravity, gauge theories and quantum foundations. This is a framework that links internal QRF perspectives via a manifestly gauge-invariant Hilbert space in the form of "quantum coordinate transformations" We reveal new effects: (i) QRFs with non-trivial orientation isotropy groups can only resolve isotropy-group-invariant properties of other subsystems; (ii) in the absence of symmetries, the internal perspective Hilbert space "rotates" through the kinematical subsystem Hilbert space as the QR
  arXiv  Detail & Related papers  (2021-10-26T16:19:24Z)
• Quantum Relativity of Subsystems [58.720142291102135]
  We show that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.
  arXiv  Detail & Related papers  (2021-03-01T19:00:01Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics [68.8204255655161]
  We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process. We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
  arXiv  Detail & Related papers  (2020-01-13T14:30:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.