The Yang-Baxter paradox

TL;DR

This paper explores a paradox in the theory of Yang-Baxter integrable systems, demonstrating that such systems can lead to contradictions when formalized as exactly-solvable, and extends the discussion to more general bosonic systems.

Contribution

It introduces formal definitions and axioms for Yang-Baxter integrable systems and reveals a paradox, providing insights into their foundational properties.

Findings

A paradox emerges in the formalization of Yang-Baxter integrable systems.

A generalization for completely integrable bosonic systems is developed.

The study highlights potential contradictions in the assumption that all such systems are exactly-solvable.

Abstract

Consider the statement "Every Yang-Baxter integrable system is defined to be exactly-solvable". To formalise this statement, definitions and axioms are introduced. Then, using a specific Yang-Baxter integrable bosonic system, it is shown that a paradox emerges. A generalisation for completely integrable bosonic systems is also developed.