@article{b4b09f29aa3b4329bfbe6b5c3227948d,
title = "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.",
keywords = "Degenerate vacuum, Dispersion relations, Nambu-Goldstone theorem, Quantum Yang-Baxter Equations, Spontaneous symmetry breaking",
author = "Ivan Arraut",
note = "Funding Information: I thank Michio Jimbo for wonderful discussions about the Quantum Yang-Baxter equations at Rikkyo University, Ikebukuro campus. I thank E.Witten as well as J. Maldacena for wonderful lectures during the conference {"}Strings 2016{"} and for wonderful discussions after. The lecture of E. Witten was fundamental for the formulation of this idea, which started during the conference Strings 2016 organized in Beijing at Tsinghua University. I thank Tadashi Takayanagi for his kind attention during my visit to the Yukawa Institute for Theoretical Physics (YITP). I thank Takahiro Nishinaka for nice discussions about these results during my visit to YITP hosted by Tadashi Takayanagi. I thank Jan de Boer for his wonderful comments and questions during my presentation in the NCTS Annual Theory Meeting, organized at the National Tsinghua University in Hsinchu, Taiwan. Finally, I thank Benjamin Basso for interesting questions and comments. This work was started under the Japan Society for the Promotion of Science (JSPS) Post-Doctoral fellow for overseas researchers and finished at the Open University of Hong Kong. This work was partially supported by the Japan Society for the Promotion of Science (JSPS), Grant No. P15322. Publisher Copyright: {\textcopyright} 2019 by the authors.",
year = "2019",
month = jun,
day = "1",
doi = "10.3390/sym11060803",
language = "English",
volume = "11",
journal = "Symmetry",
issn = "2073-8994",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "6",
}