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

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.

Published version, 22 pages

References in corpus (6)

• Supersymmetric gauge theory and the Yangian
• Nambu-Goldstone bosons and the Higgs mechanism without Lorentz invariance: Analysis based on constrained-system theory
• The Nambu-Goldstone theorem in non-relativistic systems
• The origin of the mass of the Nambu-Goldstone bosons
• Higgs Mechanism with Type-II Nambu-Goldstone Bosons at Finite Chemical Potential
• Nambu-Goldstone bosons characterized by the order parameter in spontaneous symmetry breaking

Cited by in corpus (11)

• Symmetry breaking in interacting ring-shaped superflows of Bose-Einstein condensates
• Spontaneous symmetry breaking in Quantum Finance
• The probability flow in the Stock market and Spontaneous symmetry breaking in Quantum Finance
• Gauge symmetries and the Higgs mechanism in Quantum Finance
• Topological Quantum Statistical Mechanics and Topological Quantum Field Theories
• The counting of Nambu-Goldstone bosons in a non-Hermitian field theory
• Order parameter conditions from mutual information and symmetry conditions
• Predictions of the neutrino oscillations parameters
• The solution to the Black Hole information paradox
• On the Local equivalence of the Black Scholes and the Merton Garman equations
• Hawking radiation as a manifestation of spontaneous symmetry breaking