From Yang-Mills to Yang-Baxter: In Memory of Rodney Baxter and Chen--Ning Yang
Bai-Ling Wang

TL;DR
This paper commemorates the contributions of Baxter and Yang, highlighting how their work on gauge theory and the Yang-Baxter equation reveals a shared coherence principle underlying mathematical physics.
Contribution
It synthesizes the development of gauge theory and integrability, emphasizing their interconnectedness through a unified mathematical framework.
Findings
Gauge theory's geometric structures include instantons and monopoles.
Yang-Baxter equation underpins solvable models and quantum groups.
Unified view of gauge symmetry and integrability as coherence principles.
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 underlying what is now called 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…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Quantum and Classical Electrodynamics · Nonlinear Waves and Solitons
