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Non-Abelian Gauge Structure in Stratified Quantum Normative Dynamics

Andrew H. Bond

Published Jul 19, 2026• 0 citations
Publisher

Abstract

We extend Stratified Quantum Normative Dynamics (SQND) from its original U(1) abelian gauge structure to a non-abelian framework. The key insight is that moral bonds come in distinct types that can *mix* under boundary transitions—a phenomenon requiring Yang-Mills theory. We identify **SU(2)_I × U(1)_H** as the gauge group: SU(2)_I governs *incident* relations (obligation-claim mixing) while U(1)_H tracks harm-benefit magnitude. Gauge invariance is preserved at boundaries via a **boundary Higgs mechanism**: a scalar field $\phi_{ij}$ acquires a VEV, generating effective masses for gauge bosons without explicit symmetry breaking. This mechanism admits **stratified moral phase transitions**: because critical temperature depends on stratum dimension, boundaries near decision points (low-D) melt before boundaries in deliberation space (high-D), producing a "moral triage" regime where abstract principles remain clear but concrete applications become ambiguous. We derive non-abelian junction conditions, demonstrate an area law for the Wilson loop in the strong-coupling lattice regime, and provide a complete worked example showing bond-type rotation through a moral threshold. The theory predicts enhanced contextuality quantified via the Abramsky-Brandenburger sheaf-theoretic framework. We propose five experimental protocols with explicit operationalizations, including a POVM measurement model that maps the four Hohfeldian incidents onto a 2D state space. **Keywords:** non-abelian gauge theory, Yang-Mills, stratified spaces, quantum ethics, bond algebra, Hohfeldian analysis, contextuality, Wilson loop, holonomy, boundary Higgs mechanism, moral phase transition, symmetry restoration --- Author preprint deposited for archival and citation. Draft — pending author review.

DOI
10.5281/zenodo.21435080

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We extend Stratified Quantum Normative Dynamics (SQND) from its original U(1) abelian gauge structure to a non-abelian framework. The key insight is that moral bonds come in distinct types that can mix under boundary transitions—a phenomenon requiring Yang-Mills theory. We identify SU(2)_I × U(1)_H as the gauge group: SU(2)_I governs incident relations (obligation-claim mixing) while U(1)_H tracks harm-benefit magnitude. Gauge invariance is preserved at boundaries via a boundary Higgs mechanism: a scalar field ϕij\phi_{ij}ϕij​ acquires a VEV, generating effective masses for gauge bosons without explicit symmetry breaking. This mechanism admits stratified moral phase transitions: because critical temperature depends on stratum dimension, boundaries near decision points (low-D) melt before boundaries in deliberation space (high-D), producing a "moral triage" regime where abstract principles remain clear but concrete applications become ambiguous. We derive non-abelian junction conditions, demonstrate an area law for the Wilson loop in the strong-coupling lattice regime, and provide a complete worked example showing bond-type rotation through a moral threshold. The theory predicts enhanced contextuality quantified via the Abramsky-Brandenburger sheaf-theoretic framework. We propose five experimental protocols with explicit operationalizations, including a POVM measurement model that maps the four Hohfeldian incidents onto a 2D state space. Keywords: non-abelian gauge theory, Yang-Mills, stratified spaces, quantum ethics, bond algebra, Hohfeldian analysis, contextuality, Wilson loop, holonomy, boundary Higgs mechanism, moral phase transition, symmetry restoration --- Author preprint deposited for archival and citation. Draft — pending author review.
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Abstract Quantum states can acquire a geometric phase called the Berry phase after adiabatically traversing a closed loop, which depends on the path not the rate of motion. The Berry phase is analogous to the Aharonov–Bohm phase derived from the electromagnetic vector potential, and can be expressed in terms of an Abelian gauge potential called the Berry connection. Wilczek and Zee extended this concept to include non-Abelian phases—characterized by the gauge-independent Wilson loop—resulting from non-Abelian gauge potentials. Using an atomic Bose–Einstein condensate, we quantum-engineered a non-Abelian SU(2) gauge field, generated by a Yang monopole located at the origin of a 5-dimensional parameter space. By slowly encircling the monopole, we characterized the Wilczek–Zee phase in terms of the Wilson loop, that depended on the solid-angle subtended by the encircling path: a generalization of Stokes’ theorem. This observation marks the observation of the Wilson loop resulting from a non-Abelian point source.
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