The Quantum Yang Baxter conditions: The fundamental relations behind the Nambu-Goldstone theorem

TL;DR

This paper reveals that the dynamics of Nambu-Goldstone bosons in systems with spontaneous symmetry breaking are governed by Quantum Yang-Baxter equations, providing a fundamental relation that ensures correct boson counting and dispersion.

Contribution

It introduces a novel connection between Quantum Yang-Baxter equations and the behavior of Nambu-Goldstone bosons in both relativistic and non-relativistic systems.

Findings

Quantum Yang-Baxter equations govern Nambu-Goldstone boson dynamics.

The relations ensure correct dispersion relations.

The relations guarantee proper counting of Nambu-Goldstone bosons.

Abstract

We demonstrate that when there is spontaneous symmetry breaking in any system, relativistic or non-relativistic, the dynamic of the Nambu-Goldstone bosons is governed by the Quantum Yang-Baxter equations. These equations describe the triangular dynamical relations between pairs of Nambu-Goldstone bosons and the degenerate vacuum. We then formulate a theorem and a corollary showing that these relations guarantee the appropriate dispersion relation and the appropriate counting for the Nambu-Goldstone bosons.