From Yang-Mills to Yang-Baxter: In memory of Rodney Baxter and Chen-Ning Yang

Wang Bailing

doi:10.11714/acta.snus.ZR20250270

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From Yang-Mills to Yang-Baxter: In memory of Rodney Baxter and Chen-Ning Yang

Invited review | 更新时间：2026-07-24

- From Yang-Mills to Yang-Baxter: In memory of Rodney Baxter and Chen-Ning Yang
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 65, Issue 4, Pages: 1-21(2026)
- 作者机构：
  
  澳大利亚国立大学数学科学研究所，堪培拉 2600，澳大利亚
- 作者简介：
  
  Wang Bailing（bai-ling.wang@anu.edu.au）
- 基金信息：
- DOI：10.11714/acta.snus.ZR20250270
  CLC： O189.3
- Received：31 December 2025，
  
  Revised：2026-03-13，
  
  Accepted：13 March 2026，
  
  Online First：11 May 2026，
  
  Published：25 July 2026
- 稿件说明：
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王百灵.从杨-米尔斯至杨-巴克斯特：纪念罗德尼·巴克斯特与杨振宁[J].中山大学学报(自然科学版)(中英文),2026,65(04):1-21.

Wang Bailing.From Yang-Mills to Yang-Baxter: In memory of Rodney Baxter and Chen-Ning Yang[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(04):1-21.
王百灵.从杨-米尔斯至杨-巴克斯特：纪念罗德尼·巴克斯特与杨振宁[J].中山大学学报(自然科学版)(中英文),2026,65(04):1-21. DOI： 10.11714/acta.snus.ZR20250270.

Wang Bailing.From Yang-Mills to Yang-Baxter: In memory of Rodney Baxter and Chen-Ning Yang[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(04):1-21. DOI： 10.11714/acta.snus.ZR20250270.

摘要

2025年，20世纪数学物理领域的两位巨擘罗德尼·巴克斯特与杨振宁相继离世.杨振宁通过引入非阿贝尔规范理论，以及独立提出的、奠定现称杨-巴克斯特方程基础的一致性条件，重塑了现代物理学.巴克斯特将这些条件转化为统计力学与量子可积系统中精确可解性的系统理论.本文旨在纪念巴克斯特与杨振宁，两人研究揭示了局部一致性原理如何生成全局数学结构.我们回顾了规范理论的杨-米尔斯表述、其质量阻碍及通过对称破缺的解决途径，以及由此衍生的几何框架——包括瞬子、唐纳森-弗洛尔理论、磁单极子与希钦系统.同时，我们追溯杨-巴克斯特方程从因子化散射到可解格点模型、量子群及陈-西蒙斯理论的演进历程.规范理论与可积性并非独立叙事，而是共同一致性原理的互补体现——这是从规范对称性迈向数学统一性的持续探索之旅.

Abstract

The year 2025 marked the passing of two towering figures of twentieth-century mathematical physics

Rodney Baxter and Chen-Ning Yang. Yang reshaped modern physics through the introduction of non-abelian gauge theory and

independently

through the consistency conditions that later became known as the Yang-Baxter equation. Baxter transformed those conditions into a systematic theory of exact solvability in statistical mechanics and quantum integrable systems.This article is written in memory of Baxter and Yang

whose work revealed how local consistency principles generate global mathematical structure. We review the Yang-Mills formulation of gauge theory

its mass obstruction and resolution via symmetry breaking

and the geometric framework it engendered

including instantons

Donaldson-Floer theory

magnetic monopoles

and Hitchin systems. In parallel

we trace the emergence of the Yang-Baxter equation from factorised scattering to solvable lattice models

quantum groups

and Chern-Simons theory. Rather than presenting two separate narratives

gauge theory and integrability are presented as complementary manifestations of a shared coherence principle - an ongoing journey from gauge symmetry toward mathematical unity.

关键词

Keywords

references

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