SU(2) Node Matrix Elements

This repository contains the paper "Closed-Form Matrix Elements for Arbitrary-Valence SU(2) Nodes via Generating Functionals" and its implementation as a GitHub Pages site.

Website: https://dawsoninstitute.github.io/su2-node-matrix-elements/

Abstract

We derive closed-form expressions for SU(2) operator matrix elements on arbitrary-valence nodes by extending the universal generating functional approach with source terms. Our central result is a determinant-based formula incorporating group-element dependence, which yields all matrix elements via a single Gaussian integral and hypergeometric expansion.

Repository Contents

• index.html: HTML version of the full paper with MathJax support
• _layouts/default.html: Jekyll layout template
• _includes/head.html: HTML head section with CSS and script references
• assets/css/style.scss: Main CSS for the site (processed by Jekyll)
• _config.yml: Jekyll configuration file
• Original LaTeX source files

Scope, Validation & Limitations

• Scope: The materials and numeric outputs in this repository are research-stage examples and depend on implementation choices, parameter settings, and numerical tolerances.
• Validation: Reproducibility artifacts (scripts, raw outputs, seeds, and environment details) are provided in docs/ or examples/ where available; reproduce analyses with parameter sweeps and independent environments to assess robustness.
• Limitations: Results are sensitive to modeling choices and discretization. Independent verification, sensitivity analyses, and peer review are recommended before using these results for engineering or policy decisions.