Understanding Color Confinement through Quantum Reference Frames and Relational Observables
Abstract
We present a formulation for color confinement on the basis of quantum reference frames (QRFs) and relational observables. In the QRF approach to color confinement, colored quantities are not defined as isolated local fields, but rather as relational observables with respect to a color frame or a dressing field. The Gauss law removes compactly supported local color charge from the physical bulk algebra, while boundary fluxes, Wilson lines, and holonomies may remain as semi-local data. This separates gauge invariance from frame independence. Color confinement is characterized under the fixed protocol by the absence of a finite-energy, physically accessible, asymptotically isolated nontrivial color-charged representation in the infinite volume limit. A failure to globalize a long-distance color frame is one possible mechanism contributing to this absence, which clarifies the role played by topological defects in color confinement. As concrete examples, we examine (1+1)-dimensional SU(2) Yang--Mills theory and (1+1)-dimensional U(1) gauge--Higgs model. We also take up the two-dimensional U(1) gauge--Higgs model on ℍ2 (Euclidean AdS2) and three-dimensional SU(2) gauge--Higgs model on ℍ3 (Euclidean AdS3) which are obtained based on conformal equivalence by dimensional reduction of four-dimensional SU(2) Yang--Mills theory restricted to symmetric-instanton sectors. Through explicit calculations in these examples and in controlled sectors, we provide nontrivial checks for internal consistency of the present formulation. We also discuss prospects for four-dimensional Yang--Mills theory and gauge--Higgs theories.
Related
- Radial quantization of the Schwarzschild geometry: relational observables, evaporation, and remnant state
- Constraining Modified Mass-to-Horizon Cosmology Through Primordial Inflationary Observables
- Disentangling the neutron skin of 48Ca from nuclear radius effects through 48Ca+48Ca and 48Ti+48Ti flow observables
- Cell size and confinement drive asymmetric cell division through a cortical instability
- Engineering Excitons through Polymorphism and Dimensional Confinement in Low-Dimensional Tellurium
BibTeX
@misc{kondo2026understanding,
title = {{Understanding Color Confinement through Quantum Reference Frames and Relational Observables}},
author = {Kei-Ichi Kondo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.29668},
eprint = {2606.29668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.29668},
}
RIS
TY - UNPB
TI - Understanding Color Confinement through Quantum Reference Frames and Relational Observables
AU - Kei-Ichi Kondo
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2606.29668
UR - https://arxiv.org/abs/2606.29668
AB - We present a formulation for color confinement on the basis of quantum reference frames (QRFs) and relational observables. In the QRF approach to color confinement, colored quantities are not defined as isolated local fields, but rather as relational observables with respect to a color frame or a dressing field. The Gauss law removes compactly supported local color charge from the physical bulk algebra, while boundary fluxes, Wilson lines, and holonomies may remain as semi-local data. This separates gauge invariance from frame independence. Color confinement is characterized under the fixed protocol by the absence of a finite-energy, physically accessible, asymptotically isolated nontrivial color-charged representation in the infinite volume limit. A failure to globalize a long-distance color frame is one possible mechanism contributing to this absence, which clarifies the role played by topological defects in color confinement. As concrete examples, we examine (1+1)-dimensional SU(2) Yang--Mills theory and (1+1)-dimensional U(1) gauge--Higgs model. We also take up the two-dimensional U(1) gauge--Higgs model on ℍ^2 (Euclidean AdS_2) and three-dimensional SU(2) gauge--Higgs model on ℍ^3 (Euclidean AdS_3) which are obtained based on conformal equivalence by dimensional reduction of four-dimensional SU(2) Yang--Mills theory restricted to symmetric-instanton sectors. Through explicit calculations in these examples and in controlled sectors, we provide nontrivial checks for internal consistency of the present formulation. We also discuss prospects for four-dimensional Yang--Mills theory and gauge--Higgs theories.
ER -