In this article we discuss the analogy between superfluids and a spinning thick cosmic string. We use the geometrical approach to obtain the geometrical phases for a phonon in the presence of a vortex. We use loop variables for a geometric description of Aharonov-Bohm effect in these systems. We use holonomy transformations to characterize globally the "space-time" of a vortex and in this point of view we study the gravitational analog of the Aharonov-Bohm effect in this system. We demonstrate that in the general case the Aharonov-Bohm effect has a contribution both from the rotational and the translational holonomy. We study also Berrys quantum phase for phonons in this systems.In this article we discuss the analogy between superfluids and a spinning thick cosmic string. We use the geometrical approach to obtain the geometrical phases for a phonon in the presence of a vortex. We use loop variables for a geometric description of Aharonov-Bohm effect in these systems. We use holonomy transformations to characterize globally the "space-time" of a vortex and in this point of view we study the gravitational analog of the Aharonov-Bohm effect in this system. We demonstrate that in the general case the Aharonov-Bohm effect has a contribution both from the rotational and the translational holonomy. We study also Berrys quantum phase for phonons in this systems.

arXiv:gr-qc/0401025Jan 8, 20045 citations

Artian Holonomy and the Aharonov-Bohm Effect: A QTT Source-Access Interpretation of Electromagnetic and Gravitational AB Phases

Attar Ali

Aharonov--Bohm phase as real-J holonomy Concept DOI: 10.5281/zenodo.20772090 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 This paper reads electromagnetic and gravitational Aharonov--Bohm phases as source-access holonomies. The gauge potential is the real-J dial connection; the observed complex phase is the laboratory projection $J\mapsto i$ . The compact QTT holonomy is $W_\gamma^{\mathrm{QTT}} =\exp\!\left\{J\left[ \frac{q}{\hbar c}\int_\gamma A_\mu dx^\mu - \frac{mc^2}{\hbar}\int_\gamma d\tau_{A2} \right]\right\}.$ The finite-edge admissibility gate is $\lambda_e^{\mathrm{AB}} =\frac{|\delta S_e^{\mathrm{AB}}|}{\hbar n_e} \le1.$ The standard AB equations are therefore recovered as low-density laboratory shadows of the same source holonomy. Core labels: Σ-AB-REAL-J-HOLONOMY, Σ-A2-GRAVITATIONAL-AB-ENDURANCE, Σ-A6-PHASE-DENSITY-GATE.Aharonov--Bohm phase as real-J holonomy Concept DOI: 10.5281/zenodo.20772090 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 This paper reads electromagnetic and gravitational Aharonov--Bohm phases as source-access holonomies. The gauge potential is the real-J dial connection; the observed complex phase is the laboratory projection $J\mapsto i$. The compact QTT holonomy is \[ W_\gamma^{\mathrm{QTT}} =\exp\!\left\{J\left[ \frac{q}{\hbar c}\int_\gamma A_\mu dx^\mu - \frac{mc^2}{\hbar}\int_\gamma d\tau_{A2} \right]\right\}. \] The finite-edge admissibility gate is \[ \lambda_e^{\mathrm{AB}} =\frac{|\delta S_e^{\mathrm{AB}}|}{\hbar n_e} \le1. \] The standard AB equations are therefore recovered as low-density laboratory shadows of the same source holonomy. Core labels: Σ-AB-REAL-J-HOLONOMY, Σ-A2-GRAVITATIONAL-AB-ENDURANCE, Σ-A6-PHASE-DENSITY-GATE.

Jun 20, 20262 citations

Exotic quantum holonomy induced by degeneracy hidden in complex parameter space

Sanguk Kim, Taksu Cheon, Atushi Tanaka

arXiv:0902.3315Physics Letters AFeb 26, 20108 citations

Off-diagonal quantum holonomy along density operators

Stefan Filipp, Erik Sjöqvist

arXiv:quant-ph/0403204Physics Letters AJun 1, 20055 citations

Aharonov–Bohm Holonomy as a Trinity Record: A Controlled U(1) Limit of the STO Gauge Package

EUGENE CATRAMBONE

This paper develops a controlled U(1) limit of the Trinity Scalar–Tensor–Observable (STO) gauge package by applying it to the Aharonov–Bohm effect. The goal is not to claim that Trinity is already a completed gauge theory, but to show that a well-controlled gauge phenomenon can be represented inside the Trinity formalism with precise correspondences. In the standard Aharonov–Bohm effect, a charged quantum system acquires a measurable phase shift from the electromagnetic vector potential even in a region where the local field strength vanishes. This makes the effect an important test case for the Trinity gauge package, because it distinguishes between local curvature records and global holonomy records. The paper identifies the electromagnetic U(1) potential as an Abelian sector of the Trinity awareness/selector connection A_mu^T, treats the scalar clock phi as the invariant ordering background, and shows that the standard Aharonov–Bohm phase Delta theta_AB = q Phi_B / hbar is recovered as selector holonomy in the controlled U(1) limit. The central contribution is the claim that local curvature observables of the form O(x) = C(F_mu nu^T, phi)(x) are not sufficient for all gauge phenomena. Aharonov–Bohm physics requires loop-dependent holonomy observables O_Gamma = C_Gamma(A_mu^T, phi), which are then coarse-grained into measurable detector records such as shifted interference fringes. In Trinity terms, the observed fringe displacement is interpreted as a stabilized record of scalar-clock evolution under nontrivial selector transport. The paper extends the STO gauge package by distinguishing two classes of observable records: local curvature records and global holonomy records. This result brings the Trinity/STO formalism closer to the mathematical structure of gauge theory while preserving the distinctive Trinity interpretation that observable space and time arise as projection faces of deeper scalar-clock order.This paper develops a controlled U(1) limit of the Trinity Scalar–Tensor–Observable (STO) gauge package by applying it to the Aharonov–Bohm effect. The goal is not to claim that Trinity is already a completed gauge theory, but to show that a well-controlled gauge phenomenon can be represented inside the Trinity formalism with precise correspondences. In the standard Aharonov–Bohm effect, a charged quantum system acquires a measurable phase shift from the electromagnetic vector potential even in a region where the local field strength vanishes. This makes the effect an important test case for the Trinity gauge package, because it distinguishes between local curvature records and global holonomy records. The paper identifies the electromagnetic U(1) potential as an Abelian sector of the Trinity awareness/selector connection A_mu^T, treats the scalar clock phi as the invariant ordering background, and shows that the standard Aharonov–Bohm phase Delta theta_AB = q Phi_B / hbar is recovered as selector holonomy in the controlled U(1) limit. The central contribution is the claim that local curvature observables of the form O(x) = C(F_mu nu^T, phi)(x) are not sufficient for all gauge phenomena. Aharonov–Bohm physics requires loop-dependent holonomy observables O_Gamma = C_Gamma(A_mu^T, phi), which are then coarse-grained into measurable detector records such as shifted interference fringes. In Trinity terms, the observed fringe displacement is interpreted as a stabilized record of scalar-clock evolution under nontrivial selector transport. The paper extends the STO gauge package by distinguishing two classes of observable records: local curvature records and global holonomy records. This result brings the Trinity/STO formalism closer to the mathematical structure of gauge theory while preserving the distinctive Trinity interpretation that observable space and time arise as projection faces of deeper scalar-clock order.

Apr 27, 20260 citations

J\mapsto i

. The compact QTT holonomy is

W_\gamma^{\mathrm{QTT}} =\exp\!\left\{J\left[ \frac{q}{\hbar c}\int_\gamma A_\mu dx^\mu - \frac{mc^2}{\hbar}\int_\gamma d\tau_{A2} \right]\right\}.

The finite-edge admissibility gate is

\lambda_e^{\mathrm{AB}} =\frac{|\delta S_e^{\mathrm{AB}}|}{\hbar n_e} \le1.

The standard AB equations are therefore recovered as low-density laboratory shadows of the same source holonomy. Core labels: Σ-AB-REAL-J-HOLONOMY, Σ-A2-GRAVITATIONAL-AB-ENDURANCE, Σ-A6-PHASE-DENSITY-GATE.